Question

Solve each word problem using a system of equations. Use substitution or elimination. 1. One number added to three times another number is 24. Five times the first number added to three times the other number is 36.

Answer 1

The first number is 3 and the second number is 7

Step-by-step explanation

Let the first number be x.

Let the second number be y.

The first line of the word problem is:

One number added to three times another number is 24.

This means that:

x + 3(y) = 24

=> x + 3y = 24 ______(1)

The second line of the word problem is:

Five times the first number added to three times the other number is 36.

5(x) + 3(y) = 36

5x + 3y = 36 ______(2)

Now, we have a system of equations:

x + 3y = 24 ____(1)

5x + 3y = 36 ___(2)

From the first equation, we have that:

x = 24 - 3y

Substitute that into the second equation:

5(24 - 3y) + 3y = 36

120 - 15y + 3y = 36

Collect like terms:

-15y + 3y = 36 - 120

-12y = -84

Divide through by -12:

y = -84 / -12

y = 7

Recall that:

x = 24 - 3y

=> x = 24 - 3(7) = 24 - 21

x = 3

Therefore, the first number is 3 and the second number is 7.