Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Amy wants to make scrapbooks with old family photos. An online scrapbooking company charges $24 for a basic book and $2 per page. Meanwhile, a family friend is willing to make a scrapbook for $41 plus $1 per page. For a certain number of pages, the price would be equal. How much would that cost? How many pages would that be? The scrapbook would cost $_____ if it had _____ pages.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  Amy wants to make scrapbooks with old family photos. An online scrapbooking company charges $24 for a basic book and $2 per page. Meanwhile, a family friend is willing to make a scrapbook for $41 plus $1 per page. For a certain number of pages, the price would be equal. How much would that cost? How many pages would that be?   The scrapbook would cost $_____ if it had _____ pages.

Bytelearn · Accepted Answer

Set up equations: Set up the equations based on the given information. The online scrapbooking company charges $24 for a basic book and $2 per page. If we let x represent the number of pages, then the total cost from the online company is 24 + 2x dollars. The family friend charges $41 for a basic book and $1 per page. The total cost from the family friend is 41 + x dollars. We want to find the number of pages for which the prices are equal, so we set the two expressions equal to each other: 24 + 2x = 41 + xSolve equation for x: Solve the equation for x. Subtract x from both sides to get the x terms on one side: 24 + 2x - x = 41 + x - x 24 + x = 41 Now subtract 24 from both sides to solve for x: x = 41 - 24 x = 17Determine cost for 17 pages: Determine the cost for 17 pages. We can use either of the original equations to find the total cost for 17 pages. Let's use the online company's pricing: Total cost = 24 + 2x Total cost = 24 + 2(17) Total cost = 24 + 34 Total cost = 58Verify cost with family friend: Verify the cost with the family friend's pricing. Total cost = 41 + x Total cost = 41 + 17 Total cost = 58 Since the total cost is the same with both the online company and the family friend, our solution is correct.

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