Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.A local service organization is wrapping gifts at the mall to raise money for charity. Yesterday, they wrapped 33 small gifts and 23 large gifts, earning a total of $240. Today, they wrapped 19 small gifts and 35 large gifts, and earned $334. How much did they charge to wrap the gifts?The organization charges $_____ to wrap a small gift and $_____ to wrap a large one.
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.A local service organization is wrapping gifts at the mall to raise money for charity. Yesterday, they wrapped 33 small gifts and 23 large gifts, earning a total of $240. Today, they wrapped 19 small gifts and 35 large gifts, and earned $334. How much did they charge to wrap the gifts?The organization charges $_____ to wrap a small gift and $_____ to wrap a large one.
Define Charges: Let's denote the charge for wrapping a small gift as x dollars and for a large gift as y dollars.We can write two equations based on the given information.Yesterday's earnings: 33 small gifts and 23 large gifts earned $240.Today's earnings: 19 small gifts and 35 large gifts earned $334.
Translate into Equations: Translate the given information into a system of equations.For yesterday's earnings: 33x+23y=240For today's earnings: 19x+35y=334
Solve Using Elimination: Solve the system of equations using any method. We will use the elimination method.First, we need to make the coefficients of either x or y the same in both equations. Let's multiply the first equation by 19 and the second equation by 33 to eliminate x.19(33x+23y)=19(240)33(19x+35y)=33(334)
Perform Multiplication: Perform the multiplication from Step 3.627x+437y=4560627x+1155y=11022
Subtract Equations: Subtract the second equation from the first to eliminate x.(627x+437y)−(627x+1155y)=4560−11022627x+437y−627x−1155y=−5462−718y=−5462
Solve for y: Solve for y.−718y=−5462y=−718−5462y=7.61Since the charge for wrapping a gift is unlikely to be a non-integer value, we should check our calculations for any errors.
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