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