Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. A local service organization is wrapping gifts at the mall to raise money for charity. Yesterday, they wrapped 22 small gifts and 21 large gifts, earning a total of $191. Today, they wrapped 18 small gifts and 10 large gifts, and earned $106. How much did they charge to wrap the gifts? The organization charges $_____ to wrap a small gift and $_____ to wrap a large one.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  A local service organization is wrapping gifts at the mall to raise money for charity. Yesterday, they wrapped 22 small gifts and  21 large gifts, earning a total of $191. Today, they wrapped 18 small gifts and  10 large gifts, and earned $106. How much did they charge to wrap the gifts?  The organization charges $_____ to wrap a small gift and $_____ to wrap a large one.

Bytelearn · Accepted Answer

Equations setup: Let's denote the charge for wrapping a small gift as $ s $ and for a large gift as $ l $. We can write two equations based on the given information:  1. For yesterday's earnings: $ 22s + 21l = 191 $ 2. For today's earnings: $ 18s + 10l = 106 $  These two equations form our system of equations.Elimination method: To solve this system using elimination, we need to eliminate one of the variables. We can do this by multiplying the second equation by a number that will make the coefficient of one of the variables the same in both equations. Let's multiply the second equation by 2 to match the coefficient of $ l $ in the first equation:  $ 2 \times (18s + 10l) = 2 \times 106 $  This gives us:  $ 36s + 20l = 212 $Coefficient matching: Now we have the system of equations:  1. $ 22s + 21l = 191 $ 2. $ 36s + 20l = 212 $  We can subtract the first equation from the second to eliminate $ l $:  $ (36s + 20l) - (22s + 21l) = 212 - 191 $  This simplifies to:  $ 14s - l = 21 $Subtraction correction: We made a mistake in the previous step. We should have subtracted the coefficients correctly. Let's correct that:  $ (36s + 20l) - (22s + 21l) = 212 - 191 $  This simplifies to:  $ 14s - l = 21 $  This is incorrect. We need to subtract the $ l $ terms correctly.

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