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Feb 20, 2024
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Adapted by Lumen Learning from Algebra Student Workbook by the University of Utah in association with the Utah State Office of Education is licensed under CC-BY 3.0 Assignment: Calculations and Solving Equations Scenario 1.
Write an equation for each context. Draw a model first if necessary, and make sure you define your variable and what it represents. a.
Tom has $12,484 in his bank account. Six months ago, he had $1,240. How much does Tom get paid each month if he has only deposited his monthly paycheck into his account? x= paycheck
12,484 –
1240 = 11,244 11,244/6 = 1,874
x = 1,874
b.
Sixty-five pounds of candy was divided into four different boxes. The second box contained twice the amount of the first box. The third box contained two more pounds than the first box. The last box contained one-fourth the amount in the second box. How much candy was in each box? x+2x+x+2+x/2 = 65 4x+x/2 = 65-2
4x+x/2 = 63 9x/2=63
x=63(2/9) x=14
Box 1: 14
Box 2: 28
Box 3: 16
Box 4: 7
c.
Simon is ordering equipment for his tennis team. He orders a racquet and can of three tennis balls for each player. Each can of balls costs $4. For a team of 5 players, his bill total is $415. How much does each racquet cost? 5 x 4 = 20 415 –
20 = 395 395/5= 79 Each racquet would cost $79.00
Adapted by Lumen Learning from Algebra Student Workbook by the University of Utah in association with the Utah State Office of Education is licensed under CC-BY 3.0 2.
Write a word problem or context that models the following equations. Try to make your real-life. a.
½ x + 6 = 81 ---I was buying sweaters for my family my budget is $81.00. The sweaters are on sale ½ off original price. The clerk was very helpful; I gave her a $6.00 tip. How much was each sweater?
b.
(2
t + 5) - t
= 26 ---
I had a pop-up shop selling blankets. I sold two blankets and received a $5.00 tip. One customer returned the blanket because it didn’t fit their bed. After issuing a refund for one blanket my profit was $26.00. How much was each blanket? c.
2(
L) + 3(4
L
) = 990.50 ---I purchased 2 black shirts and 3 4packs of t shirts in various colors. I paid $990.50 in total. How much did I pay for each shirt? 3.
Solve the following real-life problems. a.
The sum of two numbers is 52. One number is three less than quadruple the other number. What are the two numbers? x+4x-3=52 5x-3=52 5x=52+3 x=55/5 = 11 11+41=52 b.
Martha divides $94 amongst her four friends. Leon gets twice as much money as Kokyangwuti. Jill gets five more dollars than Leon. Isaac gets ten less dollars than Kokyangwuti. How much money does each friend get? 2x+2x+5+x-10+x = 94 6x-5=94 6x=94+5 x=99/6 Kokyangwuti = $16.50 Leon (2 x 16.50) = $33,
Adapted by Lumen Learning from Algebra Student Workbook by the University of Utah in association with the Utah State Office of Education is licensed under CC-BY 3.0 Jill (2 x 16.5) +5= $38, Isaac 16.50 - 10 = $6.5 $33+$38+$6.5+$16.5 = $94 c.
Elizabeth has $26 left after shopping at the mall. She bought 2 shirts for $22.99 each, a drink for $2.02, and 2 books for $16 each. How much money did she start with? $22.99 x 2 shirts = 45.98 $16 x 2 books = 32.00 $2.02 drink = 2.02 + $26 (still in account) Elizabeth started with $106.
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