One number exceeds another number by 6. One fourth of the sum of the two numbers is two less than the smaller. Find the numbers .

Question

One number exceeds another number by 6. One fourth of the sum of the two numbers is two less than the smaller. Find the numbers .

Answer 1

smaller is x

larger is x+6

1/4 the sum is two less than the smaller:

1/4(x+x+6) = -2 +x

1/4(2x+6)=x-2 <-- combines like terms and simplifies

(1/4)(2)(x+3) = x-2 <-- factors out 2 on the Left side

2(x+3)=4(x-2) <-- multiplies both sides by 4

2x+6 = 4x-8 <-- distributive

6 =2x-8 <-- subtracts 2x from both sides

14=2x <-- adds 8 to both sides

x=7

7 and 13

indeed (1/4)(7+13) = (1/4)(20) = 5 = 7-2

Answer 2

L = S + 6. the larger number is 6 more than the smaller number

(1/4)(L+S) = S-2 one fourth the sum is 2 less than the smaller

multiply both sides by 4

L+S = 4S-8

replace L with S+6

S+6+ S = 4S-8

2S -4S = -8-6

-2S =14

S=7 = the smaller number

L=7 +6 = 13 = the larger number

check the answer

(1/4)(L+S) = S-2

(1/4)(13+7) =7-2

20/4 = 5