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the sum of two numbers is 13. Five times the smaller is 7 less than 4 times the larger. Find the numbers.

User Azdoud
by
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1 Answer

2 votes

Answer:

5 and 8.

Explanation:

Let's represent the two numbers as variables. Let x be the smaller number, and y be the larger number.

Given information:

1. The sum of the two numbers is 13: x + y = 13.

2. Five times the smaller number is 7 less than 4 times the larger number: 5x = 4y - 7.

Now, we have a system of two equations:

1. x + y = 13

2. 5x = 4y - 7

We can solve this system of equations to find the values of x and y.

First, we can rearrange equation 1 to solve for y:

y = 13 - x

Now, substitute this value of y into equation 2:

5x = 4(13 - x) - 7

Now, solve for x:

5x = 52 - 4x - 7

5x + 4x = 52 - 7

9x = 45

x = 45 / 9

x = 5

Now that we have the value of x, we can find the value of y using the first equation:

y = 13 - 5

y = 8

So, the two numbers are 5 and 8.

User Braks
by
8.5k points

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