# Honors Algebra 2: Systems of 3 Equations Word Problems Worksheet

• Class: Honors Algebra 2
• Author: Peter Atlas
• Text: Algebra and Trigonometry: Structure and Method, Brown

Calculator: You may use a calculator for help with the arithmetic, but you may not use a systems program or matrices.

1. I find $10 on the street and run for the nearest candy store. Looking at prices, I realize that I can get 4 Ben and Jerry's Brownie Bars, 4 Snickers and 16 Tootsie Rolls, or I could purchase 5 Brownie Bars, 2 Snickers and 3 Tootsie Rolls. Or I could just settle for 9 Snickers and 100 Tootsie Rolls: that way I'd have a nickle left over. How much does a Snicker cost? 2. Solution 55 cents 3. The perimeter of parallelogram ABCD is 66 cm. E is the midpoint of side AD. If the perimeter of triangle ABE is 36 and the perimeter of trapezoid BCDE is 54, find the lengths of AB, BC, and BE. 4. Solution AB = 15, BC = 18, BE = 12 5. You have$25 to spend on picking 21 pounds of three different types of apples in an orchard. The Empire apples cost $1.40 per pound, the MacIntosh apples cost$1.10 per pound, and the Red Delicious apples cost $1.30 per pound. You want twice as many MacIntosh apples as the other two kinds combined. How many pounds of each type of apple should you buy? 6. Solution 5 pounds of Empire, 14 pounds of MacIntosh, and 2 pounds of Red Delicious. 7. An electrician, carpenter, and plumber are hired to work on a house. The electrician earns$32.50 an hour, the carpenter earns $40.75 per hour, and the plumber earns$62 an hour. Together they worked a total of 21.5 hours and earned a total of $1059.75. The carpenter worked two fewer hours than the plumber. How many hours did the electrician work? 8. Solution 10 hours 9. A gift shop has helium-filled balloons for all occasions priced according to size - small, medium, and large. Alice spent$17 for one large, two medium, and four small balloons. It cost Bryan $22 for six small, one medium, and two large balloons. For$25, Lucille got two large, three medium, and four small balloons. How much did Ken pay for three of each size?
10. Solution $28.50 11. Shelly has inherited$80,000. She invests part of her money in a certificate of deposit that produces a return of 7% per year. She divides the rest equally between a money market fund at 12% per year, and a tax-free bond at 6% per year.
1. Determine the amount of money invested in each account if Shelly receives an annual return of $6800 on all three investments. 2. Solution 20,000 in the certificate, 30,000 in the money market and 30,000 in the bond. 3. Shelly decides to invest only three-fourths of her money in the three accounts, and she receives an annual return of$5000. Determine the amount invested in each account.
4. Solution 20,000 in each.
12. A flower farmer wants to plant three types of bulbs: gladiolas, irises, and tulips. The gladiolas cost $75 per acre to plant, the irises cost$100 per acre, and the tulips cost $50 per acre. 1. The farmer wants to plant 200 acres of bulbs and spend a total of$15,000. The farmer decides to plant twice as many gladiolas as irises. Write a system of equations and find the total number of acres of each type of flower.
2. Solution 100 gladiola, 50 iris, and 50 tulip
3. The farmer decides to plant 250 acres instead, using the same amount of money. The farmer wants to keep the ratio of gladiolas to irises the same as in part a. Now how many acres of each type of flower are planted?
4. Solution 50 gladiola, 25 iris, 175 tulip
13. Jorge sold 20 new cars. He sold 4 more subcompact cars than compact cars, and one more full-sized car than compact cars. How many of each type of car did he sell?
14. Solution 5 compact, 9 subcompact, and 6 full sized.
15. A strawberry grower picked a total of 87 quarts of strawberries in 3 days. On Friday, she picked 15 more quarts than on Thursday. On Saturday, she picked 3 quarts fewer than on Friday. How many quarts of strawberries did she pick each day?
16. Solution 20 on Thursday, 35 on Friday, and 32 on Saturday.
17. A veterinarian wants to make a food mix for hamsters that contains 18.5 g of protein, 4.9 g of fat, and 13 g of moisture. She has three mixes available. The table shows the amount of protein, fat, and moisture in each mix as a percent of the total weight in grams of each mix. How many grams of each mix should she use to get the desired new mix?
Mix

Protein

(Percent)

Fat

(Percent)

Moisture

(Percent)

A
20
2
15
B
10
6
10
C
15
5
5
18. Solution 50 of A, 40 of B, and 30 of C.