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.
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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 + 0.25y = 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?
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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% Saline
X
0.40
0.40x
10% Saline
Y
0.10
0.10y
Mixture: 25%
Saline
15
0.25
3.75
Amt of Solution: x + y =15
Amt of Saline:
0.40x + 0.10y = 3.75 (after multiplying by 100) 40x+10y =375
(Remember, clear out decimals!)