the larger of two numbers is 7 less than three times the smaller number. if the sum of the numbers is 61, find the numbers

Let X = the large #

Y = the small #

We have 2 unknowns, therefore we need 2 equations to solve for them:

X + Y = 61

X = 3Y - 7

Using the substitution method we get:

X + Y = 61 original equation

(3Y - 7) + Y = 61 substituting for X

4Y - 7 = 61 combine like terms

4Y - 7 + 7 = 61 + 7 add 7 to both sides

4Y = 68 simplify

4Y/4 = 68/4 divide both sides by 4

Y = 17 solve for Y

X + Y = 61 original equation

X + 17 = 61 replace Y with 17

X + 17 - 17 = 61 - 17 subtract 17 from both sides

X = 44 solve for X

Check your answer:

X + Y = 61 X = 3Y - 7

44 + 17 = 61 44 = 3 (17) - 7

61 = 61 check! 44 = 51 - 7

44 = 44 check!

Therefore, the larger # (X) = 44 and the smaller # (Y) = 17.