Math 010 - Cooley Elementary Algebra OCC

Section 7.4 – More Applications using Systems

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Math 010 - Cooley Elementary Algebra OCC

Section 7.4 – More Applications using Systems

In this section you will be setting up and solving a system of two linear equations and two unknowns. You may

use either the Substitution Method or the Elimination Method, depending on what is easiest for you. The

answer will be the same regardless of the method you use, provided you do it correctly.

J Exercises:

Write the system of equations based off the given information.

1) Classic Total Value

A total of 400 tickets are sold raising total receipts of $2306.25. Adult tickets are $7.50 each and student tickets are $3.75 each. How many of each type of ticket was sold?

Item 1 +
Adult Tickets @ $7.50 / Item 2 =
Student Tickets @ $3.75 / Total Tickets
Number of tickets sold / + / =
Price per ticket
Total cost of tickets / + / =

2) Classic Total Value

Staples recently sold a wire-bound graph-paper notebook for $2.50 and a college-ruled notebook made

of recycled paper for $2.30. At the start of a recent semester, a combination of 50 of these notebooks

was sold for a total of $118.60. How many of each type were sold?


J Exercises:

3) Classic Solid Mixture

Peanuts sell for $1.60 per pound and cashews selling for $3.00 a pound. How many pounds of each

type are needed to obtain a 7-pound mixture selling for $2.02 per pound?

Item 1 +
Peanuts @ $1.60 / Item 2 =
Cashews @ $3.00 / Mixture
Peanut/Cashew Mix @ $2.02
Pounds of nuts / + / =
Price per pound
Total cost of nuts / + / =

4) Classic Solid Mixture

English toffee costing $1.25 per pound is mixed with caramels costing $1.50 per pound. How many

pounds of each must be used to make a 15-pound mixture costing $1.35 per pound?


J Exercises:

5) Classic Liquid Mixture

How many liters of an 18% salt solution must be added to a 61% salt solution to get 172 liters of

a 41 % salt solution?

Solution 1 +
(18%) / Solution 2 =
(61%) / Mixture
(41%)
Liters of solution / + / =
% salt
Liters of salt solution / + / =

6) Classic Liquid Mixture

Etch Clean Graphics uses one cleanser that is 25% acid and another that is 50% acid. How many

liters of each should be mixed to get 30 L of a solution that is 40% acid?

+ / =
+ / =
J Solutions:
1)
215 adult tickets and
185 child tickets / 2)
18 wire-bound and
32 college-ruled notebooks / 3)
4.9 pounds peanuts and
2.1 pounds cashews
4)
9 pounds English toffee and 6 pounds caramels / 5)
80 L of 18% solution, and
92 L of 61% solution / 6)
12 L of 25% cleaner and
18 L of 50% cleaner

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