Question

Two times a number plus ten times a second number is twenty. Thirty times the second number plus three times the first number is 45. What are the two numbers?

Answer 1

Let the 1st number is x and the 2nd number is y

Then, 2 times the 1st number = 2x, ten times the 2nd number = 10y

Then 2x + 10y = 20 (1)

Thirty times the 2nd number = 30y, 3 times the 1st number = 3x

Then 3x + 30y = 45 (2)

Now we have a system of equations to solve it

Multiply equation (1) by -3, to equate the coefficients of y in values and opposite in signs to eliminate y

-3(2x) + -3(10y) = -3(20)

-6x- 30y = -60 (3)

Add equations (2) and (3)

(3x + -6x) + (30y + -30y) = (45 + -60)

-3x + 0 = -15

-3x = -15

Divide both sides by -3

x = 5

Substitute x by 5 in equation (1) to find y

2(5) + 10y = 20

10 + 10y = 20

Subtract 10 from both sides

10 - 10 + 10y = 20 - 10

0 + 10y = 10

10y = 10

Divide both sides by 10 to find y

y = 1

The two numbers are 5 and 1