Section 7 5 System of Linear Equations Problem

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 $13. 00. 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. 10 x + 0. 25 y = 13. 00 (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) 95 x + 205 y = 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% Saline X 0. 40 x 10% Saline Y 0. 10 y Mixture: 25% Saline 15 0. 25 3. 75 Amt of Solution: x + y =15 Amt of Saline: 0. 40 x + 0. 10 y = 3. 75 (after multiplying by 100) 40 x+10 y =375 (Remember, clear out decimals!)