Question

The sum of the two numbers is 90. The larger the number is 14 more than 3 times the smaller the number. Find the numbers

x+y=_; x=_+_y

Answer 1

Smaller number = 19

Larger number = 71

x + y = 90

x = 14 + 3y

Explanation:

Let y represent the smaller number, and then represent the larger number as x, in terms of y:

Smaller number = y

Larger number = x = 3y + 14

Since the sum of the two numbers is 90, form an equation by adding them together in this notation:

y + 3y + 14 = 90

Simplify the equation:

4y + 14 = 90

4y = 76

y = 19

Therefore the smaller number is 19. Now substitute into the expression for the larger number to find its value:

x = 3(19) + 14 = 71

Now verify the two values sum to 90 like we expect:

19 + 71 = 90

Now we can use what we know to complete the equations, if x = 71:

x + y = 90 (we know they sum to 90)

x = 14 + 3y (as respresented above - multiplying by 3 and adding 14)