Worksheet: Multistep Equations

In this worksheet, we will practice solving multistep equations.

Q1:

Given that 6π‘₯+8π‘₯+3π‘₯+9π‘₯=130, find the value of 3π‘₯+6.

Q2:

If 4π‘₯+9π‘₯+3π‘₯+2π‘₯=108, what is the value of 9π‘₯+7?

Q3:

William paid $130 to subscribe to a sports club. The rate for renting a squash court is $30 per game. Since he was a student, he got a $20 discount per game. Given that William spent $360, use the equation 360=30π‘”βˆ’20𝑔+130 to determine how many games of squash he played, where 𝑔 is the number of games.

Q4:

Fourteen subtracted from three-fifths of a number is twenty-two. What is the number?

Q5:

I think of a number.

I add 13 to it and then divide by 3. The answer is 12. What number did I think of?

Q6:

Find the area of the rectangle with a width of 479 inches and a perimeter of 2223 inches.

  • A 6 2 5 2 8 1 in2
  • B 5 2 3 in2
  • C 3 1 2 6 8 1 in2
  • D 1 1 1 3 in2
  • E 4 5 1 3 in2

Q7:

Fifty-two more than one-seventh of a number is thirty-nine less than the product of two and the number.

What is the number?

Q8:

Amelia is making brooches to sell at a craft fair. It takes her 5 minutes to make a star brooch and 7 minutes to make a bow brooch.

On Saturday, she spent 434 hours making brooches. She made 3 fewer star brooches than bow brooches.

Write an equation that can be used to find 𝑦, the number of star brooches that Amelia made.

  • A 5 ( 𝑦 βˆ’ 3 ) + 7 𝑦 = 2 8 5
  • B 7 ( 𝑦 βˆ’ 3 ) + 5 𝑦 = 2 8 5
  • C 7 𝑦 + 5 ( 𝑦 + 3 ) = 2 8 5
  • D 5 𝑦 + 7 ( 𝑦 + 3 ) = 2 8 5
  • E 3 ( 𝑦 + 5 ) + 7 𝑦 = 2 8 5

Q9:

Two babies were born on the same day. One of them weighed 3 kg and the other 3.6 kg. Per week, the first baby gained 190 grams and the other gained 140 grams. At what age, in weeks, will they weigh the same?

  • A20 weeks
  • B12 weeks
  • C15 weeks
  • D10 weeks
  • E25 weeks

Q10:

Charlotte has $18 in her piggy bank and Isabella has $11. Each week, Charlotte adds 50 cents to her piggy bank, while Isabella adds $1. How many weeks will it take for both girls to have the same amount of money in their respective piggy banks? What will that amount be?

  • A 7 weeks, $18
  • B 29 weeks, $40
  • C 7 weeks, $25
  • D 14 weeks, $18
  • E 14 weeks, $25

Q11:

To roast a chicken, it should be cooked in the oven at 325∘F for 20 minutes per pound plus an additional 20 minutes.

If a chicken takes 112 hours to roast at 325∘F, write an equation that you could use to find 𝑀, the weight of the chicken.

  • A 4 0 𝑀 = 9 0
  • B 2 0 + 2 0 𝑀 = 5 0
  • C 2 0 + 𝑀 = 9 0
  • D 2 0 + 2 0 𝑀 = 3 2 5
  • E 2 0 + 2 0 𝑀 = 9 0

Q12:

For journeys between 9 pm and 7 am, a cab company charges a fixed fare of 4.50 dollars plus 40 cents per fifth of a mile.

If a passenger takes a cab at midnight and the fare was $12.10, how far did they travel?

Q13:

Matthew was collecting small change for charity. He collected cents, nickels, and dimes. He collected one and a half times as many cents as nickels and thirty-eight more dimes than nickels. There are three hundred and eighty-eight coins in his collection box.

How much money did he collect?

Q14:

One way to cook beef is to roast it in the oven at 375∘F for 15 minutes per pound plus an additional 30 minutes.

A joint of beef takes 114 hours to roast at 375∘F.

What is the weight of the joint?

Q15:

Natalie likes to do puzzles. It takes her a quarter of an hour longer to solve a hanjie than a sudoku.

Over one weekend, she spent 412 hours solving puzzles. She solved 3 sudokus and 6 hanjies.

Write an equation that can be used to find 𝑑, the amount of time it takes her to solve a hanjie puzzle.

  • A 3 ( 𝑑 βˆ’ 3 0 ) + 6 𝑑 = 4 . 5
  • B 3 ( 𝑑 βˆ’ 1 5 ) + 6 𝑑 = 4 . 5
  • C 6 ( 𝑑 βˆ’ 1 5 ) + 3 𝑑 = 2 7 0
  • D 3 𝑑 + 6 ( 𝑑 + 1 5 ) = 2 7 0
  • E 3 ( 𝑑 βˆ’ 1 5 ) + 6 𝑑 = 2 7 0

Solve your equation to find how long it takes Natalie to do a hanjie puzzle.

Q16:

Emma has saved dollars, dimes, and nickels in her money box. She has four more dollars than dimes and half as many nickels as she has dollars. She has saved $10.85 in total.

How many coins are there in her money box?

Q17:

Jennifer volunteered to bring potato chips to a school picnic. There are 6 bags of chips in a multipack, and she bought π‘₯ multipacks. She keeps 5 bags of chips for her packed lunches and takes the remaining 37 bags to the party.

How many multipacks did she buy?

Q18:

The ages of four siblings are consecutive multiples of 3, and the sum of their ages is 78. Write an equation that can be used to find 𝑛, the age of the oldest sibling.

  • A 𝑛 + ( 𝑛 + 3 ) + ( 𝑛 + 5 ) + ( 𝑛 + 7 ) = 7 8
  • B 𝑛 + ( 𝑛 βˆ’ 3 ) + ( 𝑛 βˆ’ 6 ) + ( 𝑛 βˆ’ 9 ) = 7 8
  • C 9 𝑛 + 6 𝑛 + 3 𝑛 + 𝑛 = 7 8
  • D 𝑛 + ( 𝑛 βˆ’ 3 ) + ( 𝑛 βˆ’ 5 ) + ( 𝑛 βˆ’ 7 ) = 7 8
  • E 𝑛 + ( 𝑛 + 3 ) + ( 𝑛 + 6 ) + ( 𝑛 + 9 ) = 7 8

Q19:

Daniel bought an encyclopedia with one-quarter of his birthday money. He used two-fifths of the rest to buy a plant. He has $22.50 left. How much did he pay for the plant?

Q20:

If a newborn kitten weighed 100 grams, and her weight increased by 10 grams every day, how many days would it take for her weight to triple?

Q21:

Let 𝑛 represent an unknown number. Write an equation that represents the statement β€œSixteen more than two-thirds of an unknown number is thirty-six.”

  • A 2 3 𝑛 + 3 6 = 1 6
  • B 2 3 𝑛 βˆ’ 1 6 = 3 6
  • C 2 3 𝑛 + 1 6 = 3 6
  • D 3 2 𝑛 + 1 6 = 3 6
  • E 3 2 𝑛 βˆ’ 1 6 = 3 6

Q22:

David and Chloe are traveling by bus. When they got on the bus, there were 45 people, including the two of them. At the next stop, some people got off and 5 people got on; there were then 39 people on the bus.

Write an equation that represents this situation. Let π‘₯ be the number of people who got off the bus at the stop.

  • A 3 9 βˆ’ 5 βˆ’ π‘₯ = 4 5
  • B 4 5 βˆ’ π‘₯ βˆ’ 5 = 3 9
  • C 4 5 βˆ’ π‘₯ = 3 9
  • D 3 9 + 5 βˆ’ π‘₯ = 4 5
  • E 4 5 + 5 βˆ’ π‘₯ = 3 9

Solve your equation to find π‘₯, the number of people who got off the bus.

  • A π‘₯ = 1 1
  • B π‘₯ = 6
  • C π‘₯ = 1
  • D π‘₯ = 5
  • E π‘₯ = 7 9

Q23:

A stationery store sells calculators for $7 each. Schools or colleges that make a bulk order pay full price for the first 10 calculators, and they receive a discount of $1 for each additional calculator in the same order.

A school orders π‘₯ calculators (π‘₯>10) at a cost of $112.

Write an equation that can be used to find how many calculators the school bought.

  • A 7 π‘₯ + 7 0 = 1 1 2
  • B 7 ( π‘₯ βˆ’ 1 0 ) + 7 0 = 1 1 2
  • C 6 ( π‘₯ βˆ’ 1 0 ) + 7 0 = 1 1 2
  • D ( π‘₯ βˆ’ 1 0 ) + 7 0 = 1 1 2
  • E 6 π‘₯ + 7 0 = 1 1 2

Q24:

If three times a number is added to ten, the result is the same as the sum of the number and two being multiplied by two.

What is the number?

Q25:

In order to solve the equation 4(π‘₯βˆ’3)=24, Mason wrote the next step as π‘₯βˆ’3=6. What did he do?

  • AHe divided both sides by 4.
  • BHe multiplied both sides by 3.
  • CHe multiplied both sides by 4.
  • DHe added 4 to both sides.
  • EHe subtracted 4 from both sides.

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