Shelley’s pet food store sold one customer 5 peanut butter biscuits for $3. She sold another customer 7 beef treats for $4.20. Write a proportion that compares the sales of these two items, and find the cross products. The cross products are both equal to .
Let's call the sales of peanut butter biscuits "x" and the sales of beef treats "y".
The proportion comparing the sales of these two items is:
5/3 = 7/4.20
To find the cross products, we multiply the numerator of the first fraction by the denominator of the second fraction, and multiply the denominator of the first fraction by the numerator of the second fraction:
5 * 4.20 = 21
3 * 7 = 21
Therefore, the cross products are both equal to 21.
Think about the proportion and the cross products for this problem: Shelley sold one customer 5 peanut butter biscuits for $3. She sold another customer 7 beef treats for $4.20. Because the cross products are equal, which statements are true? Select all that apply. The ratios are not equivalent. The ratios are equivalent. The ratios are not a proportion. The ratios are a proportion.
Since the cross products in the proportion are equal, the statements that are true are:
- The ratios are equivalent.
- The ratios are a proportion.
So, "The ratios are equivalent" and "The ratios are a proportion" are the correct statements.
Shelley sells 5 bone-shaped treats for $3.50. How much should she charge for a package of 12 treats?
Which proportion is needed to solve the problem?
StartFraction 5 over 12 EndFraction = StartFraction x over 3.5 EndFraction
StartFraction 12 over 3.5 EndFraction = StartFraction 5 over x EndFraction
StartFraction 3.5 over 12 EndFraction = StartFraction 5 over x EndFraction
StartFraction 5 over 3.5 EndFraction = StartFraction 12 over x EndFraction
The proportion needed to solve the problem is:
StartFraction 5 over 12 EndFraction = StartFraction x over 3.5 EndFraction
How can you check to see if two ratios form a proportion? Explain the method you used to find the answer to the previous problem.
To check if two ratios form a proportion, you can cross-multiply and see if the cross-products are equal.
In the previous problem, the given ratio was 5 treats for $3.50, which can be written as 5/3.5. We need to find the missing value for the package of 12 treats, so we set up the proportion:
StartFraction 5 over 12 EndFraction = StartFraction x over 3.5 EndFraction
To solve for x, we cross-multiply:
5 * 3.5 = 12 * x
17.5 = 12x
Finally, we divide both sides by 12 to solve for x:
17.5 / 12 = x
x ≈ 1.46
Therefore, Shelley should charge $1.46 for a package of 12 treats.
Which of the paired items from the pet store can be used to create a proportion?
3 cans of tuna for $4.50 and 5 cans of chicken for $6
2 cans of beef for $5 and 6 cans of shrimp for $15.25
5 deluxe meals for $4.75 and 10 premium meals for $9
4 cans of salmon for $9 and 6 cans of chicken for $13.50
The paired items that can be used to create a proportion are:
5 deluxe meals for $4.75 and 10 premium meals for $9
Bone-shaped treats are 5 for $3.50 at Shelley’s store and Sarah wants to buy 12. She set up and solved this proportion to find how much they would cost. Describe her error and find the correct solution.
5
3.5
=
12
x
3.5x = 60
x = $17.14
Sarah's error was that she set up the proportion incorrectly. The correct proportion should be:
StartFraction 5 over 3.5 EndFraction = StartFraction 12 over x EndFraction
Cross-multiplying the above proportion, we get:
5x = 3.5 * 12
5x = 42
To solve for x, we divide both sides by 5:
x = 42 / 5
x ≈ $8.40
Therefore, the correct cost of buying 12 bone-shaped treats at Shelley's store would be $8.40.
The following three proportions can all be used to solve the problem about Caroline's salary. Explain why the solutions to each proportion are the same. 36 4 = x 7 4 36 = 7 x 36 x = 4 7
All three proportions are equivalent and can be used to solve the problem about Caroline's salary. The solutions to each proportion will be the same because they are all different ways of expressing the same relationship between the numbers.
Let's go through each proportion to see why the solutions are the same:
1) 36/4 = x/7
Cross-multiplying, we get 36*7 = 4*x
Simplifying further, 252 = 4x
Dividing both sides by 4, we have x = 252/4
x = 63
2) 36 = 7/x
Cross-multiplying, we get 36*x = 7
Simplifying further, 36x = 7
Dividing both sides by 36, we have x = 7/36
x ≈ 0.194
3) 36x = 4/7
Dividing both sides by 36, we have x = (4/7)/36
Simplifying the right side, we get x ≈ 0.019
As we can see, in all three proportions, the solution for x is consistent: x ≈ 0.194 or approximately equal to 0.019. Hence, the solutions to all three proportions are the same.
Javed downloaded from the Internet two files that had a combined size of 696 megabytes. The size of the first file was 290 megabytes, and it took 5 minutes to download. Assuming that the files downloaded at a constant speed, how long did it take for the second file to download?
2 minutes
4 minutes
7 minutes
12 minutes
To find out the time it took for the second file to download, we can set up a proportion based on the sizes of the two files:
Size of first file / Time to download first file = Size of second file / Time to download second file
Using the given information, we can fill in the values:
290 MB / 5 minutes = ? MB / Time to download second file
To solve for the time it took to download the second file, we cross-multiply:
290 * Time to download second file = 5 * Size of second file
Now, since we know the combined size of the two files is 696 MB, we can substitute into the equation:
290 * Time to download second file = 5 * (696 - 290)
Simplifying further:
290 * Time to download second file = 5 * 406
290 * Time to download second file = 2030
Finally, we divide both sides by 290 to solve for Time to download second file:
Time to download second file = 2030 / 290 ≈ 7
Therefore, it took approximately 7 minutes for the second file to download.
What is the solution to the proportion? Round the answer to the nearest tenth if necessary.
StartFraction 52 over x EndFraction = StartFraction 9.5 over 3.25 EndFraction
x = 14.6
x = 17.8
x = 157.8
x = 169.0
To find the solution to the proportion, we can cross-multiply:
52 * 3.25 = x * 9.5
Simplifying further:
169 = 9.5x
To solve for x, we divide both sides by 9.5:
x = 169 / 9.5
x ≈ 17.8
Therefore, the solution to the proportion rounded to the nearest tenth is x = 17.8.
Why is x = 4 a solution to the proportion StartFraction 14 over x EndFraction = StartFraction 56 over 16 EndFraction?
because 56 divided by 14 is equal to 4
because 56 divided by 16 is equal to 4
because if you substitute 4 into the equation for x and cross multiply, you get 196 = 196
because if you substitute 4 into the equation for x and cross multiply, you get 224 = 224
The statement "because 56 divided by 14 is equal to 4" explains why x = 4 is a solution to the proportion StartFraction 14 over x EndFraction = StartFraction 56 over 16 EndFraction.
When we divide 56 by 14, we get 4. And by substituting x = 4 into the original proportion, both sides will be equal:
StartFraction 14 over 4 EndFraction = StartFraction 56 over 16 EndFraction
By simplifying, we have:
3.5 = 3.5
Therefore, when we substitute x = 4 into the equation and cross multiply, we get 196 = 196. This confirms that x = 4 is indeed a valid solution to the given proportion.
Which is a valid proportion?
Three-fourths = StartFraction 21 over 28 EndFraction
StartFraction 5 over 6 EndFraction = StartFraction 29 over 30 EndFraction
StartFraction 4 over 7 EndFraction = StartFraction 16 over 49 EndFraction
Two-fifths = StartFraction 12 over 15 EndFraction
A valid proportion is:
StartFraction 4 over 7 EndFraction = StartFraction 16 over 49 EndFraction
This proportion is valid because the two fractions are equal, and it is written correctly. The other options either do not have equal fractions or they are written incorrectly.
Why are the solutions to the proportions StartFraction 40 over 8 EndFraction = StartFraction x over 10 EndFraction and StartFraction x over 40 EndFraction = StartFraction 10 over 8 EndFraction the same?
because both result in the equation 8 x = 400, which simplifies to x = 5
because both result in the equation 8 x = 400, which simplifies to x = 50
because both result in the equation 40 x = 80, which simplifies to x = 2
because both result in the equation 40 x = 80, which simplifies to x = 20
The correct explanation is:
The solutions to the proportions StartFraction 40 over 8 EndFraction = StartFraction x over 10 EndFraction and StartFraction x over 40 EndFraction = StartFraction 10 over 8 EndFraction are the same because both result in the equation 8x = 400, which simplifies to x = 50.
Setting StartFraction 7 over 3 EndFraction equal to which ratio would result in a valid proportion?
StartFraction 9 over 49 EndFraction
StartFraction 18 over 42 EndFraction
StartFraction 42 over 18 EndFraction
StartFraction 49 over 9 EndFraction
Setting StartFraction 7 over 3 EndFraction equal to StartFraction 42 over 18 EndFraction would result in a valid proportion.
If Two-thirds = StartFraction x over 12 EndFraction, what is the value of x?
4
8
18
24
To solve for x in the proportion Two-thirds = StartFraction x over 12 EndFraction, we can cross-multiply:
2/3 = x/12
To find the value of x, we multiply both sides by 12:
12 * (2/3) = x
Simplifying the left side of the equation, we have:
8 = x
Therefore, the value of x is 8.
Which equation could you use to solve for x in the proportion StartFraction 4 over 5 EndFraction = StartFraction 9 over x EndFraction?
4 x = 14
4 x = 45
5 x = 13
5 x = 36
The equation that could be used to solve for x in the given proportion StartFraction 4 over 5 EndFraction = StartFraction 9 over x EndFraction is:
5x = 36
Isabella worked 50 hours over the past two weeks, and she gets paid by the hour. During the first week of the two-week span, she worked 30 hours and got paid $285.00. How much did she get paid during the second week of the two-week span?
$114.00
$190.00
$427.50
$475.50
To find out how much Isabella got paid during the second week, we can set up a proportion based on the number of hours worked and the amount of money earned:
Amount earned during the first week / Hours worked during the first week = Amount earned during the second week / Hours worked during the second week
Using the given information, we can fill in the values:
$285.00 / 30 hours = Amount earned during the second week / x hours
To solve for the amount earned during the second week, we can cross-multiply:
($285.00)(x hours) = (30 hours)(Amount earned during the second week)
Now, since we know that Isabella worked a total of 50 hours over the two weeks, we can substitute into the equation:
($285.00)(x hours) = (30 hours)(Amount earned during the second week)
($285.00)(x hours) = (50 hours - 30 hours)(Amount earned during the second week)
($285.00)(x hours) = (20 hours)(Amount earned during the second week)
Simplifying further:
285x = 20(Amount earned during the second week)
Now, to solve for the amount earned during the second week, we need to divide both sides by 20:
x = (20/285) * (Amount earned during the second week)
Simplifying further:
x ≈ 0.0702 * (Amount earned during the second week)
Since we need to find the value of the amount earned during the second week, we can set up a proportion using the given total hours:
30 hours / $285.00 = 20 hours / Amount earned during the second week
Cross-multiplying:
(30 hours)(Amount earned during the second week) = ($285.00)(20 hours)
Simplifying:
900 * Amount earned during the second week = $5700.00
Now, solving for Amount earned during the second week:
Amount earned during the second week = $5700.00 / 900
Amount earned during the second week ≈ $6.33 (rounded to the nearest cent)
Therefore, Isabella got paid approximately $6.33 during the second week of the two-week span.
In a photograph, a house is 4 inches wide and 6 inches tall. The photograph is enlarged while keeping proportional dimensions, and the width of the house in the enlarged photograph is 9 inches. What is the height of the house in the enlarged photograph?
2.7 inches
6.0 inches
11.0 inches
13.5 inches
To find the height of the house in the enlarged photograph, we can set up a proportion based on the dimensions of the original and enlarged photograph:
Original Width / Original Height = Enlarged Width / Enlarged Height
Using the given information, we can fill in the values:
4 inches / 6 inches = 9 inches / x inches
To solve for the height of the house in the enlarged photograph, we can cross-multiply:
4 inches * x inches = 6 inches * 9 inches
4x = 54
Now, we can solve for x by dividing both sides of the equation by 4:
x = 54 / 4
x = 13.5
Therefore, the height of the house in the enlarged photograph is 13.5 inches.