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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

ASiena 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?
BRen 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?

Verified Answer :

W0lf93

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 = 2612/8 = 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

calculista

Let

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

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

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

we know that

Siena's ratios

\(\frac{x}{y} =\frac{5}{8} \\\\ \frac{x}{z}= \frac{5}{12} \\ \\ \frac{y}{z} =\frac{8}{12}\)

Ren's ratios

\(\frac{x}{y} =\frac{10}{8} \\\\ \frac{x}{z}= \frac{10}{20} \\ \\ \frac{y}{z} =\frac{8}{20}\)

Part A) A. Siena wants to spend money using the same ratios as on her last trip to the carnival. If she spends $@@MATH_TOKEN_2@@ on games, how much will she spend on souvenirs?

So

@@MATH_TOKEN_3@@

@@MATH_TOKEN_4@@-----> money spent in games

substitute the value of y

@@MATH_TOKEN_5@@

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 $@@MATH_TOKEN_7@@ on souvenirs, how much will he spend on snacks?

@@MATH_TOKEN_8@@

@@MATH_TOKEN_9@@ ----> money spent in souvenirs

Substitute the value of z

@@MATH_TOKEN_10@@

therefore

the answer part B) is

Ren spend on snacks $\(2.5\)

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