PRACTICE 7-4
Use a system of equations to
solve each problem.
Your teacher is giving you a test worth 100 points containing 40
questions. There are two point questions and four point questions on the
test. How many of each type of question are on the test?
Let x be the number of four point
questions.
What are you looking for?
Let y be the number of two point
questions.
Write an equation relating the worth of each type of
question and the worth of the test.
4x +2y = 100
Write an equation relating the number of each type of question and
the total number of questions.
x +y = 40
To solve by elimination:
Multiply the second
equation
By 4.
1
4x +2y = 100
2 x + y = 40
Subtract equation 1 from equation 2.
2 4x + 4y = 160
1
Solve for y.
2 4x + 4y = 160
4x +2y = 100
2y = 60
y = 30
Substitute your answer for y back into one of the two original equations.
4x +2y = 100
x + y = 40
Remember y = 30
x + y = 40
x + 30 = 40
Solve for x.
x = 10
Summary and explanation of results.
There are 30 two-point questions and
10 four point questions on the test.
Suppose you are starting an office-cleaning service. You have spent $315
on equipment. To clean an office, you use $4 worth of supplies. You
charge $25 per office. How many offices must you clean to break even?
Let x be the number of
offices you clean.
What are you looking for?
Write an equation relating your income (I)
and the number of offices you clean.
I = 25x
Write an equation relating your expenses (E)
and the number of offices you clean.
E = 315 +4x
The break even point is the value of x
that makes income and expense the same.
To solve set I = E
I = 25x
E = 315 +4x
25x = 315 + 4x
Substitute
for I and E
21x = 315
x = 15
Solve for x.
Summary and explanation of results.
In order to break even,
you must clean 15 offices.
The math club and science club had fundraisers to buy supplies for a
hospice. The math club spent $135 buying six cases of juice and one
case of bottled water. The science club spent $110 buying four cases of
juice and two cases of bottled water. How much did a case of juice cost?
How much did a case of bottled water cost?
What are you looking for?
Let x be the cost a case of
of juice.
Write an equation for the amount
of money the Math club spent.
Let y be the cost of a case of
bottled water.
6x + y = 135
Write an equation for the amount
of money the Science club spent.
4x + 2y = 110
6x + y = 135
The best method here might be subsittution.
4x + 2y = 110
4x + 2 (135 – 6x) = 110
4x + 270 – 12x = 110
-8x + 270 = 110
-8x = -160
x = 20
y = 135 – 6x
y = 135 – 6(20)
y = 135 – 120
y = 15
Let x be the cost a case of
of juice.
Let y be the cost of a case of
bottled water.
x = 20
y = 15
The cost of a case of juice was $20
and the cost of a case of bottled water was $15.