Question

Consider the equation showing the dustributive property 5(20+__)=100+85 Enter the unknown value that would make the equation true.

Answer 1

The unknown that will make the equation true is 17

Step-by-step explanation:

let the blank space be represented by y:

`\begin{gathered} 5\mleft(20+y\mright)=100+85 \\ \text{expanding parenthesis using distributive property:} \\ 5(20)\text{ + 5(y) = 100 + 85} \\ 100\text{ + 5y = 185} \\ \end{gathered}`
`\begin{gathered} \text{subtract 100 from both sides:} \\ 100\text{ - 100 + 5y = 185 - 100} \\ 0\text{ + 5y = 85} \\ 5y\text{ = 85} \end{gathered}`
`\begin{gathered} \text{divide both sides by 5:} \\ (5y)/(5)=(85)/(5) \\ y\text{ = }17 \end{gathered}`

The unknown that will make the equation true is 17