Chloe wants to make a scrapbook with old family photos. An online scrapbooking company charges $45 plus $1 per page. Meanwhile, a family friend is willing to make a scrapbook for $9 plus $4 per page. For a certain number of pages, the prices would be equal. How many pages would that be? How much would Chloe be charged? The prices would be equal for a scrapbook that has ____ pages. Chloe would be charged $____.

Question

Chloe wants to make a scrapbook with old family photos. An online scrapbooking company charges $45 plus $1 per page. Meanwhile, a family friend is willing to make a scrapbook for $9 plus $4 per page. For a certain number of pages, the prices would be equal. How many pages would that be? How much would Chloe be charged?   The prices would be equal for a scrapbook that has ____ pages. Chloe would be charged $____.

Bytelearn · Accepted Answer

Set up equations:  Set up equations for both scrapbook costs. Online company: $ C = 45 + 1p $. Family friend: $ C = 9 + 4p $, where $ C $ is the cost and $ p $ is the number of pages. Equate expressions:  Equate the two expressions to find the number of pages where costs are equal: $ 45 + 1p = 9 + 4p $. Solve for p:  Solve for $ p $: Subtract $ 1p $ from both sides to get $ 45 = 9 + 3p $. Subtract 9:  Subtract 9 from both sides: $ 36 = 3p $. Divide by 3:  Divide both sides by 3: $ p = 12 $. Calculate cost:  Calculate the cost for 12 pages using either company's formula (since they are equal at this point): $ C = 45 + 1 \times 12 = 57 $.

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