Algebra word problem

Question

The larger of 2 numbers is 15 less than five times the smaller number. The sum of the two numbers is 87. Find the two numbers. 

Answer 1

Here's what we know:

a + b = 87 (the sum of two numbers is 87)

a = 5b - 15 (the larger # is 15 less than 5 times it)

 

Plug in the variable value:

5b - 15 + b = 87

6b -15 = 87

add 15:

6b = 102

Divide by 6:

b = 17

 

a = 5 * 17 - 15

a = 85 - 15

a = 70

 

check:

70 + 17 = 87

87 = 87

Answer 2

We want to translate the English sentences into math equations. Then we can use algebra to solve them.

 

They tell us we're thinking about two numbers, so we want two variables. Let's go with x and y.

 

They also so that the larger number is "15 less than 5 times the smaller number".

 

Let's break that down. Say the smaller number is x. (It doesn't matter which one we call x and which one we call y.)

 

5 times the smaller number--what is that? That would be 5*x.

 

Good. Okay, then what is 15 less than 5 times the smaller number? That would be 15 less than 5*x, or 5*x-15.

 

Good. Now, we're saying that expression is what the other number (y) is.

 

So we have...

y=5*x-15.

 

To say the sum of the two numbers is 87 is easy. That's just:

x+y=87

 

Now we have two equations in two variables, which we can solve. (Try subtracting the first equation from the second.)