7'4: Linear Systems and Problem Solving

1
7.4 Linear Systems and Problem Solving

• Integrated Math 2

2
Word Problems?!?!?

• A piggy bank contains 75 coins. Some are dimes
  and some are quarters. The piggy banks total
  value is 16.95. How much of each coin is in the
  bank?

Value
of coins
d
Dimes
.10d
Quarters
.25q
q
Total
75
16.95
3
Use the chart to get the system
Value
of coins
d
Dimes
.10d
Quarters
.25q
q
Total
75
16.95
The system of equations is
4
Solve by substitution
Step 2 .10d .25q 16.95 .10(-q 75) .25q
16.95 -.10q 7.5 .25q 16.95 .15q 7.5
16.95 - 7.5 -7.5 .15q
9.45 .15 .15 q
63
Step 3 d -q 75 d -(63) 75 d 12
Step 1 d q 75 - q - q d -q
75
There are 12 dimes and 63 quarters
5
Solve by Linear Combinations (elimination)
-.10d - .10q -7.5 .10d .25q 16.95
-.10 1
.15q 9.45 .15 .15
q 63
d q 75 d (63) 75 -63 -63
d 12
There are 12 dimes and 63 quarters