## Accepted Answer

Let x-------> money spent in snacksy-------> money spent in gamesz-------> money spent in souvenirswe know thatSiena'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 gamessubstitute the value of y [tex] z=\frac{12}{8} y\\ \\ z=\frac{12}{8} *26\\ \\ z=39 [/tex]thereforethe 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 souvenirsSubstitute the value of z[tex] x=\frac{1}{2} *z\\ \\ x=\frac{1}{2} *5\\ \\ x=2.5 [/tex]thereforethe answer part B) isRen spend on snacks $[tex] 2.5 [/tex]

## Suggested Answer

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