Question

The difference of two numbers is 4. If the sum of the smaller number and the square of the larger number is 86, what is the larger number?

a) 7
b) 8
c) 9
d) 10

Answer 1

To find the larger number, we can solve the given equations simultaneously. The larger number is 9.

Step-by-step explanation:

To solve this problem, let's assign variables to the two numbers. Let's call the smaller number 'x' and the larger number 'y'. According to the problem, the difference between the two numbers is 4, so we have the equation:

x - y = 4

We are also given that the sum of the smaller number and the square of the larger number is 86, so we have the equation:

x + y^2 = 86

We can solve these equations simultaneously to find the value of 'y'. Rearrange the first equation to solve for 'x':

x = y + 4

Substitute this value of 'x' into the second equation:

y + 4 + y^2 = 86

Simplify and rearrange the equation:

y^2 + y - 82 = 0

Now we can solve this quadratic equation. Factor or use the quadratic formula to find the values of 'y':

y = 9 or y = -10

Since we are looking for the larger number, we take y = 9 as the answer. Therefore, the larger number is 9.