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Worksheet: Applications of Multustep Equations

Q1:

A mobile service provider charges $11.00 plus $4.00 per minute for long distance calls, whereas another provider charges $26.00 plus $1.50 per minute. Write an equation that represents the number of minutes for which the two providers would charge the same amount, and then solve it.

  • A 4 π‘₯ βˆ’ 1 1 = 1 . 5 π‘₯ + 2 6 , π‘₯ = 6
  • B 1 1 + 4 π‘₯ = 2 6 + 1 . 5 π‘₯ , π‘₯ = 1 4
  • C 4 π‘₯ βˆ’ 1 1 = 1 . 5 π‘₯ + 2 6 , π‘₯ = 1 4
  • D 1 1 + 4 π‘₯ = 2 6 + 1 . 5 π‘₯ , π‘₯ = 6
  • E 4 π‘₯ + 1 1 = 2 6 , π‘₯ = 3

Q2:

William paid $130 to subscribe to a sports club. The rate for renting a squash court is $30 per round. Since he was a student, he got a $20 discount per round. Given that William spent $360, use the equation 3 6 0 = 3 0 𝑔 βˆ’ 2 0 𝑔 + 1 3 0 to determine how many rounds of squash he played, where 𝑔 is the number of rounds.

Q3:

One telephone service provider charges $1 plus an additional $0.50 per minute for international calls, whereas another provider charges $4 plus an additional $0.25 per minute. Write and solve an equation to find the call length for which the two telephone service providers would charge the same amount.

  • A 0 . 5 0 π‘₯ βˆ’ 1 = 0 . 2 5 π‘₯ + 4 1 2 , minutes
  • B 1 + 0 . 5 0 π‘₯ = 4 + 0 . 2 5 π‘₯ 2 0 , minutes
  • C 0 . 5 0 π‘₯ βˆ’ 1 = 0 . 2 5 π‘₯ + 4 2 0 , minutes
  • D 1 + 0 . 5 0 π‘₯ = 4 + 0 . 2 5 π‘₯ 1 2 , minutes
  • E 0 . 5 0 π‘₯ + 1 = 4 6 , minutes

Q4:

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

Q5:

Michael and Elizabeth are competing on a quiz app. Michael has 40 points already and is winning 20 points per minute; Elizabeth has 20 points already and is winning 25 points per minute.

Write an equation that can be used to find π‘š , the number of minutes until Elizabeth overtakes Michael.

  • A 2 0 + 4 0 π‘š = 2 0 + 2 5 π‘š
  • B 4 0 + 2 5 π‘š = 2 0 + 2 0 π‘š
  • C 4 0 + 2 0 π‘š = 2 5 + 2 0 π‘š
  • D 4 0 + 2 0 π‘š = 2 0 + 2 5 π‘š
  • E 2 0 + 4 0 π‘š = 2 5 + 2 0 π‘š

Q6:

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?

Q7:

For journeys between 9 am and 4 pm, a cab company charges a fixed fare of 3 dollars plus 30 cents per fifth of a mile.

A cab fare is $7.50. Write an equation that could be used to find 𝑑 , the distance traveled.

  • A 3 . 3 𝑑 = 7 . 5
  • B 0 . 3 𝑑 + 3 = 7 . 5
  • C 3 𝑑 + 1 . 5 = 7 . 5
  • D 1 . 5 𝑑 + 3 = 7 . 5
  • E 3 𝑑 + 0 . 3 = 7 . 5

Q8:

Find the area of the rectangle with a width of 4 7 9 inches and a perimeter of 2 2 2 3 inches.

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

Q9:

Twelve more than half of a number is four less than the product of two and the number.

Write an equation to represent the statement above. Let 𝑦 represent the number.

  • A 𝑦 + 1 2 = 4 βˆ’ 2 𝑦
  • B 𝑦 2 + 1 2 = 4 βˆ’ 2 𝑦
  • C 𝑦 βˆ’ 1 2 = 2 𝑦 βˆ’ 4
  • D 𝑦 2 + 1 2 = 2 𝑦 βˆ’ 4
  • E 𝑦 2 βˆ’ 1 2 = 4 𝑦 βˆ’ 2

Q10:

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?

Q11:

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 4 3 4 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 7 ( 𝑦 βˆ’ 3 ) + 5 𝑦 = 2 8 5
  • B 5 ( 𝑦 βˆ’ 3 ) + 7 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

Q12:

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

Q13:

To roast a chicken, it should be cooked in the oven at 3 2 5 ∘ F for 20 minutes per pound plus an additional 20 minutes.

If a chicken takes 1 1 2 hours to roast at 3 2 5 ∘ F , write an equation that you could use to find 𝑀 , the weight of the chicken.

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

Q14:

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?

Q15:

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?

Q16:

One way to cook beef is to roast it in the oven at 3 7 5 ∘ F for 15 minutes per pound plus an additional 30 minutes.

A joint of beef takes 1 1 4 hours to roast at 3 7 5 ∘ F .

What is the weight of the joint?

Q17:

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?

  • A 25 weeks
  • B 20 weeks
  • C 15 weeks
  • D 12 weeks
  • E 10 weeks

Q18:

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

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

Q19:

Elizabeth and Olivia are saving their allowances. Elizabeth has $100 in her account and saves $10 per month; Olivia has $50 in her account and saves $15 per month.

Write an equation that can be used to find π‘š , the number of months until their accounts have the same balance.

  • A 1 0 0 + 1 0 π‘š = 1 5 + 5 0 π‘š
  • B 1 0 + 1 0 0 π‘š = 5 0 + 1 5 π‘š
  • C 1 0 + 1 0 0 π‘š = 1 5 + 5 0 π‘š
  • D 1 0 0 + 1 0 π‘š = 5 0 + 1 5 π‘š
  • E 1 0 + 1 0 π‘š = 5 + 1 5 π‘š

Solve your equation to find π‘š .

Q20:

The sum of a number and nineteen divided by two is five more than three times the number.

Write an equation to represent the statement above. Let π‘₯ represent the number.

  • A π‘₯ + 2 1 9 = 5 + 3 π‘₯
  • B π‘₯ + 1 9 2 = 3 + 5 π‘₯
  • C π‘₯ + 1 9 = 3 + 5 π‘₯
  • D π‘₯ + 1 9 2 = 5 + 3 π‘₯
  • E π‘₯ + 1 9 2 = 5 + 3 π‘₯

Q21:

Let 𝑛 represent an unknown number. Write an equation that represents the statement β€œForty less than three times an unknown number is twenty.”

  • A 𝑛 + 4 0 = 2 0
  • B 3 𝑛 βˆ’ 2 0 = 4 0
  • C 3 𝑛 + 4 0 = 2 0
  • D 3 𝑛 βˆ’ 4 0 = 2 0
  • E 3 𝑛 + 2 0 = 4 0

Q22:

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?

Q23:

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?

Q24:

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

Q25:

William and Michael were playing a video game. Michael scored 58 959 more points than William. If their combined score was 86 905, write and solve an equation to determine William’s score.

  • A π‘˜ βˆ’ 5 8 9 5 9 = 8 6 9 0 5 , 145 864 points
  • B π‘˜ + ( π‘˜ βˆ’ 5 8 9 5 9 ) = 8 6 9 0 5 , 72 932 points
  • C π‘˜ + 5 8 9 5 9 = 8 6 9 0 5 , 27 946 points
  • D π‘˜ + π‘˜ + 5 8 9 5 9 = 8 6 9 0 5 , 13 973 points
  • E π‘˜ + π‘˜ + 8 6 9 0 5 = 5 8 9 5 9 , 72 932 points