Systems of Equations Application Problems

Master systems of equations with real-world application problems! Practice algebra skills.

1. The sum of Teresa’s and Cathy’s weight is 118 pounds. Teresa weighs 26 pounds more than Cathy. If Teresa’s weight is T and Cathy’s weight is C, which of these systems of equations best represents this relationship? T+C=118T=26 T+C=118T+26=C T+C=64T-C=26 T+C=118T=C+26 2. Your favorite restaurant has tables that seat 6 people and booths that can seat 4 people. The restaurant has 38 seating units for seating a total of 188 people. Which system of equations could you use to find the number of tables, t, and the number of booths, b, that are at the restaurant? t+b=386t+4b=188 4t=386b=188 t+b=1886t+4b=38 t+b=384t+6b=188 3. Mr. Anderson bought 8 tickets to the fair and spent a total of $30. He bought a combination of adult tickets for $5 each and child tickets $3 each. Which system of equations below will determine the number of child tickets, c, and the number of adult tickets, a, he bought? 8a+5c=30a+c=3 a+c=83a+5c=30 5a+3c=8a+c=30 5a+3c=30a+c=8 4. Ted has $6.80 in quarters and dimes. The number of dimes is 3 times the number of quarters. Which system of equations can be used to find q, the number of quarters, and d, the number of dimes, that Ted has? q=3d0.25q+0.10d=6.80 d=3+qq+d=6.80 d=3q0.25q+0.10d=6.80 d=3qq+d=6.80 5. Jose bought 9 movie tickets for a total of $54. Adult tickets cost $8 each and child tickets cost $3.50 each. How many adult tickets and child tickets did he buy? Jose bought 5 adult tickets and 4 child tickets.