One number is seven less than another. Four times the smaller is two less than twice the larger. Find the numbers.

Question

I need to know the let statements.

Answer 1

Let x and y be two numbers, then...

put the words/expressions into algebra as follows...

(1) x = y - 7 "One number is seven less than another"

(2) 4x = 2y - 2 "Four times the smaller is two less than twice the larger"

We now have 2 simultaneous equations in x and y.

4 x (1) gives 4x also so we can eliminate x by setting the two equations equal:

4 x (1) is 4x = 4y - 28

then 4y - 28 = 2y -2

=> 2y = 26

=> y = 13

now we have y, substitute in (1) to get x:

x = (13) - 7

=> x = 6

hence our two numbers are 6 and 13