Question

What two whole numbers is 352 and their sum is 38

Answer 1

The product of 2 numbers is 352 and their sum is 38

Assume that the 2 numbers are x and y, then

`\begin{gathered} x+y=38\rightarrow(1) \\ xy=352\rightarrow(2) \end{gathered}`

Use equation (1) to find y in terms of x

Subtract x from both sides

`\begin{gathered} x-x+y=38-x \\ y=38-x\rightarrow(3) \end{gathered}`

Substitute y in equation (2) by equation (3)

`x(38-x)=352`

Simplify the left side and subtract 352 from both sides

`\begin{gathered} (x)(38)-(x)(x)=352 \\ 38x-x^2=352 \\ 38x-x^2-352=352-352 \\ -x^2+38x-352=0 \end{gathered}`

Multiply each term by -1

`x^2-38x+352=0`

Factor the left side into 2 factors

`\begin{gathered} x^2=(x)(x) \\ 352=(-22)(-16) \\ (-22)(x)+(-16)(x)=-38x \\ (x-22),(x-16) \end{gathered}`

The factors are (x - 22) and (x - 16)

`\begin{gathered} x^2-38x+352=(x-22)(x-16) \\ (x-22)(x-16)=0 \end{gathered}`

Equate each factor by 0 to find x

`x-22=0`

Add 22 to each side

`\begin{gathered} x-22+22=0+22 \\ x=22 \end{gathered}`

OR

`x-16=0`

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