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The difference between two numbers is 15. If 8 is added to twice the greater number, the result is 4 less than 3 times the lesser number. Find the two numbers.

User Tpojka
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2 Answers

1 vote

Answer:


Explanation:

Let
x be the greater number and
y be the smaller number. We know that their difference is 15, so we have


x-y=15

Then, we have the following information: if we add twice the greater (2x) and 8 (2x+8), the result is 3 times the lesser (3y) minus four (3y-4). So, we have


2x+8 = 3y-4 \iff 2x-3y = -12

So, we have the follwing system:


\begin{cases} x-y=15\\2x-3y = -12\end{cases}

From the first equation, we can derive
x = y+15, and substitute this expression in the second equation to get


2(y+15)-3y = -12 \iff 2y + 30 -3y = -12 \iff -y = -42 \iff y = 42

Substitute this value for y in the first equation to get


x-42=15 \iff x=15+42 \iff x = 57

User Csl
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6 votes

Firstly, we need to write down the information given in the form of algebraic equations. We can represent our two unknown numbers, the greater and the lesser, as x and y respectively.

From the given information, we can form two equations. The first equation is from "the difference between the two numbers is 15", which gives us x - y = 15, where x is the larger number and y is the smaller one.

Also, we know that "If 8 is added to twice the greater number, the result is 4 less than 3 times the lesser number", this gives us the second equation: 2*x + 8 = 3*y - 4.

We now have a system of two equations that we can solve simultaneously:

1) x - y = 15
2) 2*x + 8 = 3*y - 4

To make it easier, let's multiply the first equation by 2, which gives us 2*x - 2*y = 30.

Now subtract the second equation (2*x + 8 = 3*y - 4) from the first (2*x - 2*y = 30), it yields: -2*y - 3*y = 30 - (-4 - 8).

This simplifies to -5y = 30 + 4 + 8, or -5*y = 42.

To get the value of y, divide by -5, therefore y = -42 / -5 = 42.

Now to find x, we can substitute y = 42 in the first equation (x - y = 15), so we get x = 42 + 15 = 57.

Hence, the greater number is 57 and the lesser number is 42.

User Edris
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