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The ratio of red jelly beans to yellow jelly beans in a dish is 3:4. If Greg eats 3 red jelly beans and 6 yellow ones, the ratio is 4:5. How many yellow jelly beans were originally in the dish?

Sagot :

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x - the number of red jelly beans
y - the number of yellow jelly beans

The ratio of red jelly beans to yellow jelly beans is 3:4.
[tex]\frac{x}{y}=\frac{3}{4} \ \ \ |\times y \\ x=\frac{3}{4}y[/tex]

If Greg eats 3 red jelly beans and 6 yellow ones, the ratio is 4:5.
[tex]\frac{x-3}{y-6}=\frac{4}{5} \ \ \ |\hbox{cross multiply} \\ 5(x-3)=4(y-6) \\ 5x-15=4y-24 \ \ \ |+15 \\ 5x=4y-9 \ \ \ |\div 5 \\ x=\frac{4}{5}y-\frac{9}{5}[/tex]

[tex] x=x \\ \frac{3}{4}y=\frac{4}{5}y-\frac{9}{5} \\ \frac{3}{4}y-\frac{4}{5}y=-\frac{9}{5} \\ \frac{15}{20}y-\frac{16}{20}y=-\frac{9}{5} \\ -\frac{1}{20}y=-\frac{9}{5} \ \ \ |\times (-20) \\ y=-\frac{9}{5} \times (-20) \\ y=9 \times 4 \\ y=36 [/tex]

There were 36 yellow jelly beans in the dish.
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