Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Vince wants to make scrapbooks with old family photos. An online scrapbooking company charges $19 for a basic book and $4 per page. Meanwhile, a family friend is willing to make a scrapbook for $37 plus $3 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 substitution, and fill in the blanks.  Vince wants to make scrapbooks with old family photos. An online scrapbooking company charges $19 for a basic book and $4 per page. Meanwhile, a family friend is willing to make a scrapbook for $37 plus $3 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

Define Variables: Let's define the variables: Let x be the number of pages in the scrapbook. Let y be the total cost of the scrapbook.  The online scrapbooking company charges $19 for a basic book and $4 per page. So the equation for the cost of the scrapbook from the online company is: y = 4x + 19Online Company Cost Equation: The family friend charges $37 for a basic book and $3 per page. So the equation for the cost of the scrapbook from the family friend is: y = 3x + 37Family Friend Cost Equation: We want to find the number of pages for which the price from both the online company and the family friend would be equal. This means we need to set the two equations equal to each other and solve for x: 4x + 19 = 3x + 37Set Equations Equal: Now we solve for x by subtracting 3x from both sides of the equation: 4x + 19 - 3x = 3x + 37 - 3x x + 19 = 37Solve for x: Next, we subtract 19 from both sides to solve for x: x + 19 - 19 = 37 - 19 x = 18Substitute x into Equation: Now that we have the value of x, we can substitute it back into either of the original equations to find the total cost y. We'll use the first equation: y = 4x + 19 y = 4(18) + 19Calculate Total Cost: Perform the multiplication and addition to find y: y = 72 + 19 y = 91Final Answer: We have found that the scrapbook would cost $91 if it had 18 pages. This answers the question prompt.

Full solution

More problems from Solve a system of equations using substitution: word problems

Related topics