There are two numbers such that the sum of tw | vedclass

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Question

(A) Let the first number be $f$ and the second number be $s$.According to the problem,we have the following system of linear equations:$2f + 3s = 100$

Vedclass · Accepted Answer

$32$

Vedclass · Answer

(A) Let the first number be $f$ and the second number be $s$.According to the problem,we have the following system of linear equations:$2f + 3s = 100$ $...(1)$$3f + 2s = 120$ $...(2)$To solve this system,multiply equation $(1)$ by $2$ and equation $(2)$ by $3$:$4f + 6s = 200$ $...(3)$$9f + 6s = 360$ $...(4)$Subtract equation $(3)$ from equation $(4)$:$(9f - 4f) + (6s - 6s) = 360 - 200$$5f = 160$$f = 32$Now,substitute $f = 32$ into equation $(1)$:$2(32) + 3s = 100$$64 + 3s = 100$$3s = 36$$s = 12$The two numbers are $32$ and $12$. Comparing these,the larger number is $32$.

There are two numbers such that the sum of twice the first number and thrice the second number is $100$ and the sum of thrice the first number and twice the second number is $120$. Which is the larger number?

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