Question 1. (3 points)
a. Show that the ratios 14/18 and 28/36 form a proportion by finding a
common multiplier.
b. Show that 14/18 and 28/36 are equal by writing them in simplest
form.
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Question 2. (4 points)
Find the unit price. Which is the better buy? Explain.
Electrical wire:
$1.89 for 3 ft.
$0.89 for 18 in.
(Remember 1 ft. = 12 in.)
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Question 3. (2 points)
A recipe for 30 cookies calls for 4 tablespoons of sugar. If you
make 40 cookies and use 5 tablespoons of sugar, will the
cookies taste the same? Explain.
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Question 4. (3 points)
A package of spaghetti weighs 238 grams. How many ounces
does the package weigh? 1 oz = 28 g.
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Question 5. (8 points)
The triangles are similar.
a. Find y using the ratio of the sides 6 cm and 8 cm:
y/24 = 68
b. Find y using the ratios of the sides 15 cm and 20 cm.
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4. I had to convert the grams into ounces so I divided 238 by 28 and got 8.5. So the package weigh 8.5 ounces
Answers??
Someone, please give the answers I'm in a rush.
i need help
Answer 1:
a. To show that the ratios 14/18 and 28/36 form a proportion, we need to find a common multiplier. We can do this by cross-multiplying.
14/18 = 28/36 (cross-multiplying)
14 * 36 = 18 * 28 (simplifying the equation)
504 = 504 (both sides are equal)
Since the cross-multiplication results in an equation where both sides are equal, we can conclude that the ratios 14/18 and 28/36 form a proportion.
b. To show that 14/18 and 28/36 are equal by writing them in simplest form, we need to reduce the fractions to their simplest form.
14/18 = 7/9 (dividing both numerator and denominator by the greatest common divisor, which is 2)
28/36 = 7/9 (dividing both numerator and denominator by the greatest common divisor, which is 4)
Since both fractions, 7/9 and 7/9, are equal, we can conclude that 14/18 and 28/36 are equal.
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Answer 2:
To find the unit price and determine which option is the better buy, we need to compare the cost per unit length for both electrical wire options.
Option 1: $1.89 for 3 ft.
Option 2: $0.89 for 18 in. (Remember 1 ft. = 12 in.)
First, we need to convert the cost of Option 2 to the cost per foot:
Option 2:
$0.89 for 18 in.
$0.89 for 18/12 ft. (since 1 ft. = 12 in.)
$0.89 for 1.5 ft.
Now we can compare the unit prices:
Option 1: $1.89 divided by 3 ft. = $0.63 per ft.
Option 2: $0.89 divided by 1.5 ft. = $0.59 per ft.
Since the unit price for Option 2 is lower ($0.59 per ft. compared to $0.63 per ft.), Option 2 is the better buy.
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Answer 3:
To determine if the cookies will taste the same when making 40 cookies with 5 tablespoons of sugar instead of the original recipe of 30 cookies with 4 tablespoons of sugar, we need to consider the ratio of sugar to cookies.
Original recipe:
30 cookies require 4 tablespoons of sugar.
Ratio of sugar to cookies: 4 tablespoons / 30 cookies
New recipe:
40 cookies with 5 tablespoons of sugar.
Ratio of sugar to cookies: 5 tablespoons / 40 cookies
To compare the ratios, we can simplify both fractions:
4/30 = 2/15 (by dividing both numerator and denominator by the greatest common divisor, which is 2)
5/40 = 1/8 (by dividing both numerator and denominator by the greatest common divisor, which is 5)
Since the ratios 2/15 and 1/8 are different, the cookies made with 5 tablespoons of sugar will not taste the same as the original recipe. There will be a difference in the amount of sugar per cookie.
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Answer 4:
To convert the weight of the package of spaghetti from grams to ounces, we can use the conversion factor given: 1 oz = 28 g.
So, to find the weight of the package in ounces, we divide the weight in grams by the conversion factor:
Weight in ounces = 238 g / 28 g/oz
Weight in ounces = 8.5 oz
Therefore, the package of spaghetti weighs 8.5 ounces.
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Answer 5:
a. To find y using the ratio of the sides 6 cm and 8 cm, we can set up a proportion:
y/24 = 6/8
To solve for y, we can cross-multiply:
8y = 6 * 24
8y = 144
y = 144/8
y = 18
Therefore, using the ratio of sides 6 cm and 8 cm, y = 18.
b. To find y using the ratios of the sides 15 cm and 20 cm, we can set up a similar proportion:
y/24 = 15/20
To solve for y, we can again cross-multiply:
20y = 15 * 24
20y = 360
y = 360/20
y = 18
Therefore, using the ratio of sides 15 cm and 20 cm, y = 18.