Question

The smaller of two numbers is 12 less than a larger four times the larger exceeds three times the smaller by 90. Find the numbers.

Answer 1

By setting up a system of equations and solving for two unknowns, the larger number is found to be 54 and the smaller number is 42.

The question asks us to find two numbers where the smaller number is 12 less than the larger number, and four times the larger number exceeds three times the smaller number by 90. To solve this problem, we can set up a system of equations.

Step-by-step Solution:

1. Let the smaller number be s and the larger number be l.
2. According to the problem, s = l - 12.
3. The second condition states that 4l = 3s + 90.
4. Substitute s from the first equation into the second to get 4l = 3(l - 12) + 90.
5. Simplify and solve the equation: 4l = 3l - 36 + 90, so l = 54.
6. Now that we have l, we can find s by substituting back into the first equation: s = 54 - 12 = 42.

Therefore, the larger number is 54 and the smaller number is 42.