Worksheet: Writing and Evaluating Algebraic Expressions

In this worksheet, we will practice writing algebraic expressions and evaluating them for specific values of their variables.

Q1:

Evaluate π‘š+π‘˜, given that π‘š=7 and π‘˜=15.

Q2:

Consider the shown trapezoid.

Write an expanded expression for its area. Simplify the expression, if possible.

  • A6π‘Ž+4
  • Bπ‘Ž+5π‘ŽοŠ¨
  • Cπ‘Ž+4
  • Dπ‘Ž+5π‘Žβˆ’4
  • Eπ‘Žβˆ’5π‘Ž+4

The given trapezoid is the cross section of a prism of length 2π‘Žβˆ’5. Write an expanded expression for the volume of the prism. Simplify the expression, if possible.

  • A2π‘Žβˆ’15π‘Ž+33π‘Žβˆ’20
  • B2π‘Ž+5π‘Žβˆ’13π‘Žβˆ’4
  • C5π‘Žβˆ’13π‘Žβˆ’4
  • D2π‘Ž+5π‘Žβˆ’13π‘ŽοŠ©οŠ¨
  • E2π‘Žβˆ’13π‘Žβˆ’4

Q3:

Consider the shown trapezoid.

Write an expanded expression for its area. Simplify the expression, if possible.

  • A6π‘Ž+4
  • Bπ‘Ž+5π‘ŽοŠ¨
  • Cπ‘Ž+4
  • Dπ‘Žβˆ’5π‘Ž+4
  • Eπ‘Ž+5π‘Žβˆ’4

The given trapezoid is the cross section of the given prism of length 2π‘Žβˆ’5.

Write an expanded expression for the volume of the prism. Simplify the expression, if possible.

  • A2π‘Žβˆ’13π‘Žβˆ’4
  • B2π‘Ž+5π‘Žβˆ’13π‘Žβˆ’4
  • C5π‘Žβˆ’13π‘Žβˆ’4
  • D2π‘Žβˆ’15π‘Ž+33π‘Žβˆ’20
  • E2π‘Ž+5π‘Žβˆ’13π‘ŽοŠ©οŠ¨

Q4:

Evaluate π‘šΓ—5 if π‘š=7.

Q5:

Using π‘₯ to represent the cost of a notebook and 𝑦 to represent the cost of a folder, write an expression for the cost of 3 notebooks and 2 folders. Then, find the total cost, given that the notebooks are $1.69 each and the folders are $0.59 each.

  • A5π‘₯𝑦, $4.99
  • B2π‘₯+3𝑦, $5.15
  • C6π‘₯𝑦, $5.98
  • D3π‘₯+2𝑦, $6.25
  • E3π‘₯+2𝑦, $5.15

Q6:

Given that a day consists of 24 hours, write an expression that relates the number of days in terms of hours, and then determine how many hours there are in 3 days.

  • A24(𝑛+1), 96 hours
  • B24𝑛, 72 hours
  • C24𝑛, 144 hours
  • D24+𝑛, 27 hours
  • E24+𝑛, 21 hours

Q7:

What is the area of a square of perimeter 7π‘₯?

  • A4916π‘₯
  • B494π‘₯
  • C4916π‘₯
  • D49
  • E49π‘₯

Q8:

A club is producing posters. If the cost of making one poster is 10 LE and the shipping cost of an order of any size is 27 LE, what is the total cost of producing and shipping an order of π‘₯ posters?

  • A(10π‘₯+27)LE
  • Bο€Ό10π‘₯+27LE
  • C(27π‘₯+10)LE
  • Dο€»π‘₯10+27LE
  • E(10π‘₯βˆ’27)LE

Q9:

Write two equivalent expressions for the area of the following figure.

  • A20(π‘₯+8), 20π‘₯+160
  • B10(π‘₯+8), π‘₯+80
  • C20(π‘₯+8), 20π‘₯+28
  • D10(π‘₯+8), 10π‘₯+18
  • E10(π‘₯+8), 10π‘₯+80

Q10:

Translate the following verbal expression into an algebraic one, and then simplify it: Four sets of the sum of a number and eleven are added to three times the same number.

  • A4(π‘₯+11)+3, 4π‘₯+47
  • B4(π‘₯+11)+3π‘₯, 7π‘₯+44
  • C4(π‘₯+11)+3π‘₯, 7π‘₯+15
  • D4(π‘₯+11)+3, 4π‘₯+18
  • E(4π‘₯+11)+3π‘₯, 7π‘₯+11

Q11:

A rectangle’s dimensions are (8π‘₯+4) length units and (16π‘₯+6) length units. Express the perimeter in terms of π‘₯ and calculate the perimeter when π‘₯=1.

  • A(24π‘₯+2) length units, 26 length units
  • B(48π‘₯+20) length units, 68 length units
  • C(48π‘₯βˆ’4) length units, 44 length units
  • D(24π‘₯+10) length units, 34 length units

Q12:

Sophia received $75 on her birthday to buy a gift. She bought three new pairs of pants for 𝑠 dollars each. Write an expression to represent the amount of money she has left. Given that each pair costs $21, how much money does she have left?

  • A75βˆ’21𝑠, $12
  • B75βˆ’π‘ , $54
  • C3𝑠, $63
  • D75βˆ’3𝑠, $12
  • E75+3𝑠, $138

Q13:

An online art store sells paint brushes for $12 each and oil colors for $10 each and charges $7.5 per order for shipping. Denoting the number paint brushes by 𝑝 and that of oil colors by 𝑐, write an expression that represents the total cost, and then calculate the cost of one order of 7 brushes and 9 oil colors.

  • A(12×𝑝)+(10×𝑐), $174
  • B(14.5×𝑝)+(16.5×𝑐), $339
  • C(7×𝑝)+(9×𝑐)+7.5, $181.5
  • D(12×𝑝)+(10×𝑐)+7.5, $181.5
  • E(19.5×𝑝)+(17.5×𝑐), $294

Q14:

Knowing that a year consists of 52 weeks, make a table to find the algebraic expression that relates the number of weeks to the number of years 𝑛. If the Greens have been living in a neighborhood for 19 years, determine that duration in weeks.

  • A52(𝑛+1), 1,040 weeks
  • B52(π‘›βˆ’1), 936 weeks
  • C52+𝑛, 71 weeks
  • D52𝑛, 988 weeks
  • E52+(π‘›βˆ’1), 70 weeks

Q15:

A farmer harvested 36 pounds of cotton this year. Given that there are 16 ounces in 1 pound, determine, by making a table, the algebraic expression that relates the number of ounces to that of pounds, and find how many ounces of cotton the farmer harvested.

  • A16+𝑛, 52 oz
  • B16(𝑛+1), 592 oz
  • C16𝑛, 576 oz
  • D16(π‘›βˆ’1), 560 oz
  • E16+𝑛, 51 oz

Q16:

David spent 540 seconds jogging. Make a table to determine the algebraic expression that relates the number of seconds𝑛 to that of minutes, given that there are 60 seconds in 1 minute. Then, determine how many minutesDavid spent jogging.

  • A𝑛÷60, 9 min
  • B𝑛÷6, 90 min
  • C60+𝑛, 600 min
  • D60𝑛, 8 min
  • Eπ‘›βˆ’60, 480 min

Q17:

If a rectangle has a length of 13 centimeters and a width of 12 centimeters, determine, in the simplest form, what fraction of the perimeter the width is.

  • A2512
  • B625
  • C1225
  • D256
  • E1350

Q18:

A pizza delivery company offers 2 medium pizzas and a 1-liter bottle of soda for $12. They offer 2 sides and a dessert for $6.

Benjamin ordered 8 medium pizzas, 4 sides, 4 liters of soda, and 2 desserts. What is the cost of his order?

Q19:

A group of friends is planning to go to a concert, and the cost in dollars for 𝑛 tickets is 21𝑛. Given that as few as 14 people or as many as 31 people might go, find the minimum and maximum costs that the group of friends might pay.

  • A$651, $945
  • B$35, $45
  • C$294, $651
  • D$294, $434
  • E$35, $52

Q20:

For a marathon, an athlete practiced on a track that is π‘š miles long. She ran for 5 laps each on Monday and on Wednesday and 4 laps on Friday. On Sunday, she ran for 18 miles. Write an expression in the simplest form that represents the total distance the athlete ran during her practice.

  • A14π‘š+18
  • B9π‘š+18
  • C9π‘šβˆ’18
  • D20π‘š+18
  • E13π‘š+18

Q21:

The height of the Empire State Building is 164 meters more than 3 times the height of the Statue of Liberty. Let β„Ž be the height of the Statue of Liberty. Write an expression that represents the height of the Empire State Building in terms of β„Ž.

  • A3β„Ž+164
  • B3(β„Ž+164)
  • C164βˆ’3β„Ž
  • D164β„Ž+3
  • E3β„Žβˆ’164

Q22:

You have $100 in the bank. Each day, you deposit $10 into your account. Write an expression for your balance after 𝑑 days.

  • A110𝑑
  • B10π‘‘βˆ’100
  • C10𝑑+100
  • D100𝑑+10
  • E10𝑑

Q23:

Admission to a museum costs $5 per person. A family has a coupon for a discount of $8. There are 𝑝 people in the family. Write an expression that represents how much the family pays.

  • A5𝑝
  • B5π‘βˆ’8
  • C5𝑝8
  • D5π‘βˆ’40
  • E8+5𝑝

Q24:

At noon, a barista notices that she has $20 in her tip jar. In the afternoon, her average tip is $0.50 per customer. Write an expression to describe how much money she will have in her tip jar at the end of her shift if she serves 𝑛 more customers.

  • A$(20𝑛)
  • B$(0.5π‘›βˆ’20)
  • C$(0.5𝑛+20)
  • D$(20π‘›βˆ’0.5)
  • E$(20𝑛+0.5)

Q25:

A shop sells chocolates for 26 LE a kilogram and boxes for 6 LE. A boy bought π‘₯ kg of chocolate and a box. Write an expression for the amount he paid.

  • A(32π‘₯)LE
  • B(26π‘₯+6)LE
  • C(26π‘₯βˆ’6)LE
  • D(6π‘₯βˆ’26)LE
  • E(6π‘₯+26)LE

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