One number is 28 more than three times another number. If each number were multiplied by 4, their difference would be 232. What are the numbers?

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giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll note the numbers as x and y.

We'll put as x the number that is 28 more than three times y.

We'll write the sentence mathematically:

x = 28 + 3y (1)

Now, we'll write mathematically the other constraint from enunciation:

4(x - y) = 232

We'll divide by 4;

x - y = 58

x = 58 + y (2)

We'll put (1) = (2):

28 + 3y = 58 + y

We'll isolate y to the left side:

3y - y = 58 - 28

2y = 30

y = 15

x = 58 + y

x = 58 + 15

x = 73

The numbers are: x = 73 and y = 15.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

Let the two numbers be x and y. Then x =  28+3y by first condition.

When each number is multiplied by 4, then their difference  is 4(x-y) which is said to be 232.

So 4(x-y) = 232. We substitute x= 28+3y in 4(x-y) = 232.:

4{28+3y-y) =232.

We divide by 4:

28+2y = 232/4 = 58.

2y = 58-28 = 30.

So y = 30/2 = 15.

So x= 28+3y = 28+3*15 = 73.

Therefore the two numbers are  73 and 15.

Therefore x= 73 and y = 15.

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