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 34 small gifts and 48 large gifts, earning a total of $486. Today, they wrapped 28 small gifts and 50 large gifts, and earned $484. 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 34 small gifts and  48 large gifts, earning a total of $486. Today, they wrapped 28 small gifts and  50 large gifts, and earned $484. 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: Let's define the variables for the amount charged to wrap a small gift and a large gift. Let x be the amount charged for wrapping a small gift, and y be the amount charged for wrapping a large gift.Write equations for days: Now we can write two equations based on the information given for the two days. For yesterday, the equation is 34x + 48y = 486. For today, the equation is 28x + 50y = 484.Use elimination method: We will use the elimination method to solve this system of equations. To eliminate one of the variables, we can multiply the first equation by 28 and the second equation by 34, so that the coefficients of x in both equations are the same.Multiply first equation: Multiplying the first equation (34x + 48y = 486) by 28, we get: 28 * 34x + 28 * 48y = 28 * 486 952x + 1344y = 13608Multiply second equation: Multiplying the second equation (28x + 50y = 484) by 34, we get: 34 * 28x + 34 * 50y = 34 * 484 952x + 1700y = 16456Subtract equations: Now we subtract the second equation from the first to eliminate x: (952x + 1344y) - (952x + 1700y) = 13608 - 16456 0x + (1344y - 1700y) = -2848 -356y = -2848Solve for y: Divide both sides by -356 to solve for y: y = -2848 / -356 y = 8Substitute back to solve x: Now that we have the value for y, we can substitute it back into one of the original equations to solve for x. We'll use the first equation: 34x + 48y = 486. 34x + 48 * 8 = 486 34x + 384 = 486Subtract to solve x: Subtract 384 from both sides to solve for x: 34x = 486 - 384 34x = 102Divide to solve x: Divide both sides by 34 to solve for x: x = 102 / 34 x = 3Final solution: We have found that the organization charges $3 to wrap a small gift and $8 to wrap a large one.

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