Section 7'4 Applications of Linear Systems

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Section 7.4Applications of Linear Systems
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Methods of Solving Linear Systems
Graphing A useful method for approximating a
solution, checking the reasonableness of a
solution and providing a visual model.
Substitution A useful method when one of the
variables has a coefficient of 1 or -1.
Elimination A useful method when none of the
variables has a coefficient of 1 or -1.
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Example 4
A group of 40 children attended a baseball game
on a field trip. Each child received either a
hot dog or a bag of popcorn. Hot dogs were 2.25
and popcorn was 1.75. If the total bill was
83.50, how many hot dogs were bought?
Let x of hot dogs bought.
Let y of popcorns bought.
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Example 4(continued)
Step 1
Step 3
Step 2
Solution (27, 13)
27 hot dogs were bought.
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Example 4(continued)
Solution Checks
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Example 5
A health food store mixes granola that costs them
4 per pound and raisins that cost 2 per pound
to make a total of 25 pounds of raisin granola.
How many pounds of raisins should they include if
they want the mixture to cost them a total of 80.
Let x pounds of granola
Let y pounds of raisins
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Example 5(continued)
and
Step 1
Step 3
Step 2
Solution (15, 10)
15 pounds of granola.
10 pounds of raisins.
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Example 5(continued)
Solution Checks
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Example 6
A toy maker produces wooden trains and planes.
Each train requires 3 oz. of paint and each plane
requires 5 oz. of paint. The toy maker wants to
make 14 toys. How many of each can he make if he
has a total of 64 ounces of paint.
Let x number of trains
Let y number of planes
10
Example 6 (continued)
and
Step 1
Step 2
-3
Step 3
Step 4
y 11
Solution 3 trains 11 planes
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Example 6(continued)
Solution Checks
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Example 8
An assortment of nuts costs 36. A special brand
of pecans selling at 7.50 per pound is mixed
with almonds selling at 6.00 per pound. How
many pounds of each can be found in a 5 pound
package?
Let x pounds of pecans
Let y pounds of almonds
13
Example 8(continued)
and
Step 1
Step 3
Step 2
Solution (4, 1)
4 pounds of pecans 1 pound of almonds
14
Example 8(continued)
and
Solution Checks