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 15 small gifts and 33 large gifts, earning a total of $357. Today, they wrapped 35 small gifts and 33 large gifts, and earned $437. How much did they charge to wrap the gifts?The organization charges _____ to wrap a small gift and _____ to wrap a large one.
Q. 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 15 small gifts and 33 large gifts, earning a total of $357. Today, they wrapped 35 small gifts and 33 large gifts, and earned $437. How much did they charge to wrap the gifts?The organization charges _____ to wrap a small gift and _____ to wrap a large one.
Define Costs: Let's denote the cost to wrap a small gift as x dollars and the cost to wrap a large gift as y dollars. We can write two equations based on the information given for the two days.Yesterday's earnings: 15 small gifts and 33 large gifts for $357.Today's earnings: 35 small gifts and 33 large gifts for $437.
Write Equations: Translate the information into two equations.For yesterday: 15x+33y=357For today: 35x+33y=437
Eliminate Variable: To use elimination, we need to eliminate one of the variables. We can eliminate y by subtracting the first equation from the second equation because they both have the same coefficient for y.
Subtract Equations: Subtract the first equation from the second equation to eliminate y.(35x+33y)−(15x+33y)=437−35735x+33y−15x−33y=437−35720x=80
Solve for x: Solve for x by dividing both sides of the equation by 20. 2020x=2080x=4
Substitute x: Now that we have the value for x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation: 15x+33y=357.15(4)+33y=35760+33y=357
Solve for y: Subtract 60 from both sides of the equation to solve for y.33y=357−6033y=297
Solve for y: Subtract 60 from both sides of the equation to solve for y.33y=357−6033y=297Divide both sides of the equation by 33 to find the value of y.3333y=33297y=9
More problems from Solve a system of equations using elimination: word problems