Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Brian works in an amusement park and is helping decorate it with strands of lights. This morning, he used a total of 48 strands of lights to decorate 3 bushes and 3 trees. This afternoon, he strung lights on 4 bushes and 5 trees, using a total of 75 strands. Assuming that all bushes are decorated one way and all trees are decorated another, how many strands did Brian use on each? Brian 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.  Brian works in an amusement park and is helping decorate it with strands of lights. This morning, he used a total of 48 strands of lights to decorate 3 bushes and  3 trees. This afternoon, he strung lights on 4 bushes and  5 trees, using a total of 75 strands. Assuming that all bushes are decorated one way and all trees are decorated another, how many strands did Brian use on each?  Brian decorated every bush with _____ strands of lights and every tree with _____ strands.

Bytelearn · Accepted Answer

Define Equations: Let's denote the number of strands used on each bush as b and the number of strands used on each tree as t. We can write two equations based on the information given.Morning Decoration: The first equation comes from the morning's decoration: 3 bushes and 3 trees use a total of 48 strands. 3b + 3t = 48Afternoon Decoration: The second equation comes from the afternoon's decoration: 4 bushes and 5 trees use a total of 75 strands. 4b + 5t = 75System of Equations: We now have a system of equations: 3b + 3t = 48 4b + 5t = 75 We can solve this system using either substitution or elimination. Let's use the elimination method.Elimination Method: To eliminate one of the variables, we can multiply the first equation by 4 and the second equation by 3 to make the coefficients of b the same. (4)(3b + 3t) = (4)(48) (3)(4b + 5t) = (3)(75)Multiply Equations: Multiplying out the equations, we get: 12b + 12t = 192 12b + 15t = 225Subtract Equations: Now we subtract the first new equation from the second new equation to eliminate b. (12b + 15t) - (12b + 12t) = 225 - 192Solve for t: Simplifying the subtraction, we get: 15t - 12t = 225 - 192 3t = 33Substitute t: Dividing both sides by 3 to solve for t, we find: t = 33 / 3 t = 11Solve for b: Now that we have the value for t, we can substitute it back into one of the original equations to solve for b. Let's use the first equation: 3b + 3(11) = 48Simplify the equation by multiplying 3 times 11: 3b + 33 = 48Subtract 33 from both sides to solve for b: 3b = 48 - 33 3b = 15Divide both sides by 3 to find the value of b: b = 15 / 3 b = 5

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