Section 7.5: System of Linear Equations & Problem Solving 3 examples of how to set-up and solve word problems using systems of equations.

Example 1: Misha has a total of 100 coins, all of which are either dimes or quarters. The total value of the coins is $ Find the number of each type of coin. Come up with two equations. 1 equation relating # of coins 1 equation relating total value Good practice to say “Let x = # of dimes and let y = # of quarters” (# of coins) x + y = 100 (total value) 0.10x y = (Hint: How would you clear out decimals? In this case, multiply equation 2 by 100 to ALL terms. Look at the system carefully and decide which method you’ll use to solve: Addition method OR Substitution method?

Example 2: A customer recently purchased 16 tickets with seats in either the lower level ($205) or upper level ($95). He paid a total of $2,620 for the tickets. How many lower level and upper level tickets did he buy? Let x = # of upper level tickets Let y = # of lower level tickets (# of tickets)x + y = 16 (Price/cost)95x + 205y = 2620 Decide which method you will use: Addition/Substitution?

Example 3: Elise Everly is preparing 15 liters of a 25% saline solution. Elise has two other saline solutions of strengths 40% and 10%. Find the amount of 40% and 10% solution she should mix to get 15 liters of 25% solution (Hint: Make a chart!) Amount of solution (L)(times) % saline= Amount of saline 40% SalineX x 10% SalineY y Mixture: 25% Saline Amt of Solution: x + y =15 Amt of Saline:0.40x y = 3.75 (after multiplying by 100)  40x+10y =375 (Remember, clear out decimals!)