Question

Whats the answer for each box

Answer 1

`\begin{aligned}x+(x+1)+(x+2)&=66 \\ 3x + 3 &= 66 \\ \underline{\ \ \ \ -3} &\ \ \ \ \underline{\ -3} \\ 3x &= 63 \\ x &= 21\end{aligned}`

Explanation:

Line 1

Since the friends' ages are consecutive, they are 1 whole number apart. Therefore, the friends ages will be:

`x`,
`x+1`, and
`x + 2`

Note: We can represent the oldest friend's age as:
`(x + 1) + 1`, but this simplifies to
`x + 2`.

Line 2

First, we can regroup like terms using the associate property of addition. Then, we can combine like terms to simplify the expression.

`\begin{aligned}x + (x + 1) + (x + 2) &= (x + x + x) + (1 + 2)\\&= 3x + 3\end{aligned}`

Lines 3 & 4

To solve for x from the equation:

`3x + 3 = 66`

we need to subtract 3 from both sides to isolate the x's on one side, then divide both sides by 3 (x's coefficient) to solve for one x.

Line 5

Doing the operations in lines 3 and 4, we get a solution for x:

`x = 21`