Question

The product of two numbers is 1856. The sum is ninety. What is the difference of these two numbers?A.30B.28C.26D.24

Answer 1

Given:

• Product of two numbers = 1856

,

• Sum of two numbers = 90

Let's find the difference of these two numbers.

Let x represent the bigger number.

Let y represent the smaller number.

We have the system of equations:

• xy = 1856

,

• x + y = 90

Let's solve the system simultaneously using substitution method.

Rewrite the second equation for x:

`x=90-y`

Substitute (90-y) for x in equation 1:

`(90-y)y=1856`

Apply distributive property:

`90y-y^2=1856`

Equate the equation to zero and factor the left side:

`\begin{gathered} 90y-y^2-1856=0 \\ \\ -y^2+90y-1856=0 \\ \\ -(y^2-90y+1856)=0 \\ \\ -(y-58)(y-32)=0 \end{gathered}`

Equate the individual factors to zero and solve for y:

`\begin{gathered} y-58=0 \\ \text{Add 58 to both sides:} \\ y-58-58=0+58 \\ y=58 \\ \\ \\ y-32=0 \\ \text{Add 32 to both sides:} \\ y-32+32=0+32 \\ y=32 \end{gathered}`

Therefore, we have:

y = 32 and 58

Since y is the smaller number, let y be 32.

x is the greater number.

x = 58.

Therefore, the two numbers are:

58 and 32.

To find the difference of the two numbers, subtract the smaller number from the greater number.

58 - 32 = 26

Therefore, the difference of the two numbers is 26.

ANSWER:

C. 26