Question

Solve each of the following by using a proportion. 1. One out of every five people who buy ice cream buys vanilla ice cream. If a store sells 125 ice cream cones in one day, about how many will be vanilla? 2. Taxes on a house assessed at $64,000 are $1500 a year, If the assessment is raised to $85,000 and the tax rate did not change, how much would the taxxes be? 3. I have a map where Indy and Ft. Wayne are 3 centimeters apart. Kokomo and Indy are 1.5 cm apart on the map. If I know that Indy and Ft. Wayne are really 120 miles apart, how far would Indy and Kokomo be in real life? 4. A clock can make 1 full rotation with its hand in 1 minute. How many rotations would it make in 1 hour? 5. Let us imagine that your MATH 123 book cost $45 to print. How much does it cost per page? (Hint: you will need information about your book to calculate this!)

Answer 1

1) 25 ice cream cones

2) $1992.18 in taxes.

3) 60 miles apart.

4) 60 rotations

5)45/p where p is the number of pages.

Explanation:

1) One out of every five people who buy ice cream buys vanilla ice cream. If a store sells 125 ice cream cones in one day, about how many will be vanilla?

We need to solve this problem using a proportion and solving for x:

`(1)/(5)=(x)/(125)  \\x=125/5\\x=25`

25 ice cream cones will be vanilla.

2. Taxes on a house assessed at $64,000 are $1500 a year, If the assessment is raised to $85,000 and the tax rate did not change, how much would the taxes be?

`(64000)/(1500) =(85000)/(x) \\x=1500(85000)/64000\\x=1992.18`

Taxes would be $1992.18

3. I have a map where Indy and Ft. Wayne are 3 centimeters apart. Kokomo and Indy are 1.5 cm apart on the map. If I know that Indy and Ft. Wayne are really 120 miles apart, how far would Indy and Kokomo be in real life?

To solve this, first we have to remember that 1 mile equals 160934 cms. Therefore, 120 miles would be 19312080 cms.

`(3)/(1.5) =(19312080)/(x) \\x=19312080(1.5)/3\\x= 9656040`

Indy and Kokomo are 9656040 cms apart, this equals 9656040/160934 = 60 miles apart.

4. A clock can make 1 full rotation with its hand in 1 minute. How many rotations would it make in 1 hour?

1 hour has 60 minutes, therefore the proportion would be:

`(1)/(1)=(x)/(60)  \\x=60(1)/(1)\\x=60`

It makes 60 rotations in 1 hour.

5. Let us imagine that your MATH 123 book cost $45 to print. How much does it cost per page?

I don't know how many pages your book has, let's call p the number of pages it has.

`(45)/(p) =(x)/(1) \\x=45/p`.

It would cost 45/p where p is the total of pages of your book.