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Two numbers have a sum of 37, and 4 times the

first number minus the second number is equal
to 43. What are the two numbers?

1 Answer

6 votes

Answer:

16 and 21

Explanation:

To find the two numbers, let's assign variables to them. Let's call the first number "x" and the second number "y".

According to the problem, we know two things:

1. The sum of the two numbers is 37: x + y = 37.

2. 4 times the first number minus the second number is equal to 43: 4x - y = 43.

To solve this system of equations, we can use the method of substitution. We'll solve one equation for one variable and substitute it into the other equation.

Let's solve the first equation for "x":

x = 37 - y.

Now, substitute this value of "x" into the second equation:

4(37 - y) - y = 43.

Simplifying the equation, we get:

148 - 4y - y = 43.

148 - 5y = 43.

Next, let's isolate "y" by subtracting 148 from both sides:

-5y = 43 - 148.

-5y = -105.

Dividing both sides by -5, we get:

y = -105 / -5.

y = 21.

Now that we have the value of "y", we can substitute it back into the first equation to find "x":

x + 21 = 37.

x = 37 - 21.

x = 16.

Therefore, the two numbers are 16 and 21.

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