LoanWambach483idn
Answered

Discover new knowledge and insights with IDNLearn.com's extensive Q&A platform. Find the solutions you need quickly and accurately with help from our knowledgeable community.

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 :

W0lf93idn
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
Calculistaidn

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]

We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.