Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ Two friends visited a taffy shop. Rachel bought $2$ kilograms of strawberry taffy and $5$ kilograms of banana taffy for $\$43$ . Next, Devon bought $1$ kilogram of strawberry taffy and $1$ kilogram of banana taffy for $\$11$ . How much does the candy cost? $\newline$ A kilogram of strawberry taffy costs $\$$ _, and a kilogram of banana taffy costs $\$$ _.

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Grade 8

Solve a system of equations using elimination: word problems

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Two friends visited a taffy shop. Rachel bought

2

kilograms of strawberry taffy and

5

kilograms of banana taffy for

\$43

. Next, Devon bought

1

kilogram of strawberry taffy and

1

kilogram of banana taffy for

\$11

. How much does the candy cost?

\newline

A kilogram of strawberry taffy costs

\$

_____, and a kilogram of banana taffy costs

\$

_____.

Equations Setup: Let's denote the cost of a kilogram of strawberry taffy as $S$ dollars and the cost of a kilogram of banana taffy as $B$ dollars. We can write two equations based on the information given: $\newline$ $1$ . For Rachel's purchase: $2S + 5B = 43$ $\newline$ $2$ . For Devon's purchase: $S + B = 11$
Elimination Method: To solve the system using elimination, we want to eliminate one of the variables. We can multiply the second equation by $2$ to align the coefficients of $S$ : $2(S + B) = 2(11)$ $2S + 2B = 22$
New System of Equations: Now we have a new system of equations: $\newline$ $1$ . $2S + 5B = 43$ $\newline$ $2$ . $2S + 2B = 22$ $\newline$ We can subtract the second equation from the first to eliminate $S$ : $\newline$ $(2S + 5B) - (2S + 2B) = 43 - 22$
Subtraction to Eliminate S: Performing the subtraction gives us: $\newline$ $2S + 5B - 2S - 2B = 43 - 22$ $\newline$ $5B - 2B = 21$ $\newline$ $3B = 21$
Solving for B: Dividing both sides of the equation by $3$ to solve for B: $\newline$ $\frac{3B}{3} = \frac{21}{3}$ $\newline$ $B = 7$ $\newline$ So, a kilogram of banana taffy costs $\$7$ .
Substitute $B$ to Find $S$ : Now that we know the cost of banana taffy, we can substitute $B = 7$ into one of the original equations to find $S$ . We'll use the second equation: $\newline$ $S + B = 11$ $\newline$ $S + 7 = 11$
Substitute B to Find S: Now that we know the cost of banana taffy, we can substitute $B = 7$ into one of the original equations to find $S$ . We'll use the second equation: $\newline$ $S + B = 11$ $\newline$ $S + 7 = 11$ Subtracting $7$ from both sides to solve for $S$ : $\newline$ $S + 7 - 7 = 11 - 7$ $\newline$ $S = 4$ $\newline$ So, a kilogram of strawberry taffy costs $\$4$ .