Name ________________________________
Unit 6 – Systems of Equations/Inequalities
Date _________________
Math 8H
Aim #58 Classwork: Systems of Equations Word Problems (Day 1)
Solve each word problem algebraically by setting up a system of equations. Show all work!
1) The sum of two positive numbers is 14. If the larger number exceeds the smaller number by 9, what are the
numbers?
2) At Gino’s Pizzeria, the total price for 5 large pizza pies and 2 medium pizza pies is $81.50. The total for 4 large
pizza pies and 3 medium pizza pies is $78.50. What is the price of a large pie? What is the price of a medium pie?
3) A soda machine contains 20 coins. Some of the coins are nickels and the rest are quarters. If the value of the
coins is $4.40, then find the number of coins of each kind.
4) Find two numbers such that the sum of the first and twice the second is 11 and the sum of the second and eight
times the first is 16.
5) A store sells Brazilian coffee for $10 per pound and Columbian coffee for $14 per pound. If they decide to
make a 150 pound blend of the two and sell it for $11 per pound, how much of each type of coffee should be used?
6) Pam has two part time jobs. At one job, she works as a cashier and makes $8 per hour. At the second job, she
works as a tutor and makes $12 per hour. One week she worked 30 hours and made $268. How many hours did she
spend at each job?
7) Lulu tells her little brother, Jack, that she is holding 20 coins all of which are dimes and quarters. They have a
value of $4.10. How many of each coin does Lulu have?
8) The manager at a community pool is looking over receipts. On a certain Monday, the pool had 32 children and 17
adults, which brought in $83. That same Tuesday, 32 children and 47 adults came to the pool, which brought in
$173. What are the admission prices for children and adults?
9) A math test is worth 100 points and has 25 questions. There are multiple-choice questions worth 3 points each
and short essay questions worth 8 points each. How many short essay questions are on the test?
10) The sum of two numbers is 104. The larger number is 1 less than twice the smaller number. Find the numbers.
11) Eight roses and nine carnations cost $3.35. At the same prices, one dozen roses and 5 carnations cost $3.75.
Find the cost of a rose and the cost of a carnation.
12) The larger of two numbers decreased by the smaller is 5. Twice the smaller number increased by the larger
number is 41. What is the number?
13) The price of a sweater is $5 less than twice the price of a shirt. If four shirts and three sweaters cost $275,
find the price of each shirt and each sweater.
14) Find two numbers such that the sum of the first and three times the second is 5 and the sum of the second
and two times the first is 8.
15) When Angelo cashed his check for $170, the bank teller gave him a total of 12 bills, some $10 bills and some
$20 bills. How many bills of each kind did Angelo receive?
Review: Simplify in scientific notation:
(9.4 x 108) – (1.3 x 105)