Question

Hans is thinking of two positive numbers. He says, "If we double the first number and " triple the second number, the sum is 36."

Answer 1

2x+3y=36

3y=36-2x

3y\2=36-x

Answer 2

Therefore, the first number is 18 and the second number is 0.

Explanation:

Let x be the first number and y be the second number. We are given that:

2x + 3y = 36

We can solve for x and y using substitution or elimination. Let's use substitution.

Solve the first equation for x:

x = 18 - (3/2)y

Substitute this expression for x into the second equation:

2(18 - (3/2)y) + 3y = 36

Simplify and solve for y:

36 - 3y + 3y = 36

y = 0

Since y is 0, we can substitute this value into the first equation to find x:

2x + 3(0) = 36

2x = 36

x = 18