Tanner and his sister, Mona, both brought gummy bears on a family car trip. At the beginning of the drive, Mona had twice as many gummy bears as Tanner. While on the road, Mona ate $23$ of her gummy bears and Tanner ate $7$ of his. When they got to their destination, Tanner realized they each had the same number of gummy bears left. $\newline$ Which equation can you use to find $t$ , the number of gummy bears Tanner had at the beginning of the drive? $\newline$ Choices: $\newline$ (A) $t - 2 = 23t - 7$ $\newline$ (B) $2t - 23 = t - 7$ $\newline$ How many gummy bears did Tanner have at the beginning of the drive? $\newline$ ____ gummy bears

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Solve linear equations with variables on both sides: word problems

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Q. Tanner and his sister, Mona, both brought gummy bears on a family car trip. At the beginning of the drive, Mona had twice as many gummy bears as Tanner. While on the road, Mona ate

23

of her gummy bears and Tanner ate

7

of his. When they got to their destination, Tanner realized they each had the same number of gummy bears left.

\newline

Which equation can you use to find

t

, the number of gummy bears Tanner had at the beginning of the drive?

\newline

Choices:

\newline

(A)

t - 2 = 23t - 7

\newline

(B)

2t - 23 = t - 7

\newline

How many gummy bears did Tanner have at the beginning of the drive?

\newline

____ gummy bears

Set up equation: Let's set up the equation based on the problem statement. Mona started with twice as many gummy bears as Tanner, so if Tanner had $t$ gummy bears, Mona had $2t$ gummy bears. After eating some, Tanner had $t - 7$ left, and Mona had $2t - 23$ left. They ended up with the same amount, so the equation is: $\newline$ $t - 7 = 2t - 23$
Solve for t: Now, solve for t. Subtract $t$ from both sides: $\newline$ $t - 7 - t = 2t - 23 - t$ $\newline$ $-7 = t - 23$
Isolate $t$ : Next, add $23$ to both sides to isolate $t$ :\-7 + 23 = t - 23 + 23 $16 = t$