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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

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?

Sagot :

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 = 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
calculista

Let

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

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

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

we know that

Siena's ratios

[tex] \frac{x}{y} =\frac{5}{8} \\\\ \frac{x}{z}= \frac{5}{12} \\ \\ \frac{y}{z} =\frac{8}{12} [/tex]

Ren's ratios

[tex] \frac{x}{y} =\frac{10}{8} \\\\ \frac{x}{z}= \frac{10}{20} \\ \\ \frac{y}{z} =\frac{8}{20} [/tex]

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

So

[tex] \frac{y}{z} =\frac{8}{12} \\ \\ 12y=8z\\ \\ z=\frac{12}{8} y [/tex]

[tex] y=26 [/tex]-----> money spent in games

substitute the value of y

[tex] z=\frac{12}{8} y\\ \\ z=\frac{12}{8} *26\\ \\ z=39 [/tex]

therefore

the answer Part A) is

Siena spend on souvenirs $[tex] 39 [/tex]

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

[tex] \frac{x}{z} =\frac{10}{20} \\ \\ 20x=10z\\ \\ x=\frac{1}{2} *z [/tex]

[tex] z=5 [/tex] ----> money spent in souvenirs

Substitute the value of z

[tex] x=\frac{1}{2} *z\\ \\ x=\frac{1}{2} *5\\ \\ x=2.5 [/tex]

therefore

the answer part B) is

Ren spend on snacks $[tex] 2.5 [/tex]

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