Mathematics
Jamie6916
15

The sum of two numbers is 150. The ratio of the same two numbers is 3:2. Find the bigger number. Please show work and explain. (:

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(1) Answers
Collegegirl763

x, y - the numbers The sum of two numbers is 150. [latex]x+y=150 \ \ \ |-y \\ x=150-y[/latex] The ratio of the two numbers is 3:2. [latex]\frac{x}{y}=\frac{3}{2} \ \ \ |\times y \\ x=\frac{3}{2}y[/latex] Set both expressions equal to each other: [latex]x=x \\ 150-y=\frac{3}{2}y \ \ \ |+y \\ 150=\frac{3}{2}y+y \\ 150=\frac{3}{2}y+\frac{2}{2}y \\ 150=\frac{5}{2}y \ \ \ |\times \frac{2}{5} \\ 150 \times \frac{2}{5}=y \\ 30 \times 2=y \\ y=60 \\ \\ x=150-y=150-60=90[/latex] The numbers are 60 and 90. The bigger number is 90.

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