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 48 small gifts and 29 large gifts, earning a total of $318. Today, they wrapped 19 small gifts and 43 large gifts, and earned $315. 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 48 small gifts and  29 large gifts, earning a total of $318. Today, they wrapped 19 small gifts and  43 large gifts, and earned $315. 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

Define variables: Define the variables for the cost to wrap a small gift and a large gift. Let x be the cost to wrap a small gift, and y be the cost to wrap a large gift.Write first day's earnings equation: Write the equation for the first day's earnings. 48 small gifts and 29 large gifts earned a total of $318. 48x + 29y = 318Write second day's earnings equation: Write the equation for the second day's earnings. 19 small gifts and 43 large gifts earned a total of $315. 19x + 43y = 315Decide variable to eliminate: Decide which variable to eliminate. We can choose to eliminate either x or y. To make calculations simpler, we will eliminate x by multiplying the first equation by 19 and the second equation by 48, because 19 and 48 are the coefficients of x in the two equations.Multiply equations by coefficients: Multiply the first equation by 19 and the second equation by 48. First equation: (48x + 29y) * 19 = 318 * 19 Second equation: (19x + 43y) * 48 = 315 * 48Write new equations after multiplication: Write the new equations after multiplication. First equation: 912x + 551y = 6042 Second equation: 912x + 2064y = 15120Subtract equations to eliminate x: Subtract the second equation from the first to eliminate x. (912x + 551y) - (912x + 2064y) = 6042 - 15120Perform subtraction to solve for y: Perform the subtraction to solve for y. 912x + 551y - 912x - 2064y = 6042 - 15120 551y - 2064y = 6042 - 15120 -1513y = -9078Solve for y: Solve for y. y = -9078 / -1513 y = 6Substitute y into original equation: Substitute y = 6 into one of the original equations to solve for x. Using the first day's equation: 48x + 29(6) = 318Perform substitution and solve for x: Perform the substitution and solve for x. 48x + 174 = 318 48x = 318 - 174 48x = 144Divide to find x: Divide both sides by 48 to find x. x = 144 / 48 x = 3Final solution: We found x = 3 and y = 6. The organization charges $3 to wrap a small gift and $6 to wrap a large one.

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