Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Finn works in an amusement park and is helping decorate it with strands of lights. This morning, he used a total of 60 strands of lights to decorate 5 bushes and 3 trees. This afternoon, he strung lights on 5 bushes and 2 trees, using a total of 50 strands. Assuming that all bushes are decorated one way and all trees are decorated another, how many strands did Finn use on each? Finn decorated every bush with _____ strands of lights and every tree with _____ strands.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  Finn works in an amusement park and is helping decorate it with strands of lights. This morning, he used a total of 60 strands of lights to decorate 5 bushes and  3 trees. This afternoon, he strung lights on 5 bushes and  2 trees, using a total of 50 strands. Assuming that all bushes are decorated one way and all trees are decorated another, how many strands did Finn use on each?  Finn decorated every bush with _____ strands of lights and every tree with _____ strands.

Bytelearn · Accepted Answer

Define variables: Let's define variables for the number of strands used per bush and per tree. Let b = number of strands per bush Let t = number of strands per treeWrite first equation: Write the first equation based on the morning decoration. 5 bushes and 3 trees use 60 strands. 5b + 3t = 60Write second equation: Write the second equation based on the afternoon decoration. 5 bushes and 2 trees use 50 strands. 5b + 2t = 50Elimination method: Solve the system of equations using the substitution or elimination method. We will use the elimination method. To eliminate one of the variables, we can multiply the second equation by -1.5 and add it to the first equation. -1.5(5b + 2t) = -1.5(50) -7.5b - 3t = -75 Now add this to the first equation: 5b + 3t = 60 -7.5b - 3t = -75 ----------------- -2.5b = -15Solve for b: Solve for b. -2.5b = -15 Divide both sides by -2.5 to find b. b = -15 / -2.5 b = 6Substitute to solve for t: Substitute the value of b back into one of the original equations to solve for t. Using the second equation: 5b + 2t = 50 5(6) + 2t = 50 30 + 2t = 50 2t = 50 - 30 2t = 20 Divide both sides by 2 to find t. t = 20 / 2 t = 10

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