Student Question

The sum of two numbers is 20. The larger number is four less than twice the smaller number. What are the two numbers?

Expert Answers

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Let x be the bigger number and let y be the smaller number.

x + y = 20

x = 2y -4

So now we substitute this value of x into the original equation.

2y - 4 + y = 20

3y - 4 = 20

3y = 24

y = 8

If y = 8, then

x = 12

because x + y must equal 20.  To check this, let us see if these values work with the other equation

12 = (2*8) - 4

12 = 16 - 4

True -- so this is correct.

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Assume that the numbers are x and y.

==> x+y=20....(1)

x=2y-4

Substitute with x=2y-4 in equation(1):

(2y-4)+y=20

3y-4 =20

ADD 4:

3y=24

Divide by 3:

y=24/3=8

==> x=2(8)-4 = 12

To check:\

12+8 = 20

12= 2(8)-4 =12

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