Joy is a contestant on the kids' game show, Spend or Switch! When she makes it up on stage, host Guy Granger takes out a stack of one hundred-dollar bills. He divides the bills evenly among all $8$ contestants on stage. Each contestant receives $3$ one hundred-dollar bills. $\newline$ Which equation can you use to find the number of bills $b$ in Guy Granger's stack? $\newline$ Choices: $\newline$ (A) $\frac{b}{8} = 3$ $\newline$ (B) $b - 8 = 3$ $\newline$ (C) $b + 8 = 3$ $\newline$ (D) $8b = 3$ $\newline$ Solve this equation for $b$ to find the number of bills in Guy Granger's stack. $\newline$ ____ bills $\newline$

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Grade 6

Solve one-step equations: word problems

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Q. Joy is a contestant on the kids' game show, Spend or Switch! When she makes it up on stage, host Guy Granger takes out a stack of one hundred-dollar bills. He divides the bills evenly among all

8

contestants on stage. Each contestant receives

3

one hundred-dollar bills.

\newline

Which equation can you use to find the number of bills

b

in Guy Granger's stack?

\newline

Choices:

\newline

(A)

\frac{b}{8} = 3

\newline

(B)

b - 8 = 3

\newline

(C)

b + 8 = 3

\newline

(D)

8b = 3

\newline

Solve this equation for

b

to find the number of bills in Guy Granger's stack.

\newline

____ bills

\newline

Understand the problem: Understand the problem. $\newline$ Joy receives $3$ one hundred-dollar bills, and this amount is evenly divided among all $8$ contestants. We need to find the total number of bills $b$ that Guy Granger had originally.
Set up the equation: Set up the equation. $\newline$ If each contestant receives $3$ bills and there are $8$ contestants, the total number of bills is the number of contestants multiplied by the number of bills each contestant receives. The equation that represents this situation is $\frac{b}{8} = 3$ , where $b$ is the total number of bills.
Solve the equation for b: Solve the equation for b. $\newline$ To find $b$ , we need to multiply both sides of the equation by $8$ to isolate $b$ on one side. $\newline$ $\frac{b}{8} \times 8 = 3 \times 8$ $\newline$ $b = 24$
Verify the solution: Verify the solution. $\newline$ If we substitute $b$ with $24$ into the equation $\frac{b}{8} = 3$ , we get: $\newline$ $\frac{24}{8} = 3$ $\newline$ $3 = 3$ $\newline$ This shows that our solution is correct.