Question

The table shows the amount that each person spend on snacks, games, and souvenirs the las time they went to the carnival.

Sinea- snacks $5/ games $8/ souvenirs $12
Ren- snacks $10/ games $8/ souvenirs $20

A. Siena wants to spend money using the same ratios as on her last trip to the carnival. If she spends $26 on games, how much will she spend on souvenirs?
B. Ren wants to spend money using the same ratios as on his last trip to the carnival. If he spends $5 on souvenirs, how much will he spend on snacks?

Answer 1

This is a problem of proportions. The initial data gives you the ratios, then you can use them to build proportions for each case. A. Siena's game to souvenier ratio is 8/12 then you can build the proportion: 8/12 = 26/x and solve for x: x = 26*12/8 = 17.33 B. Ren's souvenier to snacks ratio is 20 / 10, the the proportion is 20 / 10 = 5 / x => x = 5 * 10 / 20 = 2.5

Answer 2

Let

x-------> money spent in snacks

y-------> money spent in games

z-------> money spent in souvenirs

we know that

Siena's ratios

`(x)/(y) =(5)/(8) \\\\ (x)/(z)= (5)/(12) \\ \\ (y)/(z) =(8)/(12)`

Ren's ratios

`(x)/(y) =(10)/(8) \\\\ (x)/(z)= (10)/(20) \\ \\ (y)/(z) =(8)/(20)`

Part A) A. Siena wants to spend money using the same ratios as on her last trip to the carnival. If she spends $
`26` on games, how much will she spend on souvenirs?

So

`(y)/(z) =(8)/(12) \\ \\ 12y=8z\\ \\ z=(12)/(8) y`

`y=26`-----> money spent in games

substitute the value of y

`z=(12)/(8) y\\ \\ z=(12)/(8) *26\\ \\ z=39`

therefore

the answer Part A) is

Siena spend on souvenirs $
`39`

Part B) Ren wants to spend money using the same ratios as on his last trip to the carnival. If he spends $
`5` on souvenirs, how much will he spend on snacks?

`(x)/(z) =(10)/(20) \\ \\ 20x=10z\\ \\ x=(1)/(2) *z`

`z=5` ----> money spent in souvenirs

Substitute the value of z

`x=(1)/(2) *z\\ \\ x=(1)/(2) *5\\ \\ x=2.5`

therefore

the answer part B) is

Ren spend on snacks $
`2.5`