Question

the ratios of girls to boys in a student basketball league is 5:6. juan says that there must be exactly 11 students in the league. is juans statement correct

Answer 1

`\bf \cfrac{5x}{6x}\implies \cfrac{5}{6}~~ratio~\hfill \stackrel{x=1}{\cfrac{5\cdot 1}{6\cdot 1}}\implies \cfrac{5}{6} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{x=20}{\cfrac{5\cdot 20}{6\cdot 20}}\implies \cfrac{100}{120}\implies \cfrac{5}{6}~\hfill \stackrel{x=100000}{\cfrac{5\cdot 100000}{6\cdot 100000}}\implies \cfrac{500000}{600000}\implies \cfrac{5}{6}`

yes, he's correct, IF our multiplying value of "x" is 1, however, a ratio of 5/6 is also true for 100/120 or 500000/600000, and any other value up to infinity for that matter.

so it could be 11, or it could be much more.

Answer 2

False

Explanation:

girls : boys : total

5 : 6 :11

Multiply each term by 2

10: 12 :22

Ratio of girls to boys

10:12

Divide by 2

5:6

The ratio of girls to boys is still 5:6 but the total students is 22