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Lesson: Applications of Multistep Equations

Sample Question Videos

Worksheet • 25 Questions • 21 Videos

Q1:

Given that 6 π‘₯ + 8 π‘₯ + 3 π‘₯ + 9 π‘₯ = 1 3 0 , find the value of 3 π‘₯ + 6 .

Q2:

If 4 π‘₯ + 9 π‘₯ + 3 π‘₯ + 2 π‘₯ = 1 0 8 , what is the value of 9 π‘₯ + 7 ?

Q3:

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

  • A , 13 973 points
  • B , 72 932 points
  • C , 72 932 points
  • D , 27 946 points
  • E , 145 864 points

Q4:

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

Q5:

Nabil 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 Nabil spent $360, use the equation to determine how many rounds of squash he played, where is the number of rounds.

Q6:

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

Q7:

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

Q8:

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

Write an equation that can be used to find , the number of minutes until Mona overtakes Fady.

  • A
  • B
  • C
  • D
  • E

Q9:

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?

Q10:

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

Q11:

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

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

Q12:

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?

Q13:

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

Q14:

Dina 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 hours making brooches. She made 3 fewer star brooches than bow brooches.

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

  • A
  • B
  • C
  • D
  • E

Q15:

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

Q16:

Sally has $18 in her piggy bank and Nada has $11. Each week, Sally adds 50 cents to her piggy bank, while Nada 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?

  • A14 weeks, $25
  • B7 weeks, $25
  • C7 weeks, $18
  • D14 weeks, $18
  • E29 weeks, $40

Q17:

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

Q18:

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

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

  • A 3.8 miles
  • B 19 miles
  • C 6.05 miles
  • D 7.6 miles
  • E 12.10 miles

Q19:

Sameh 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?

Q20:

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?

Q21:

Yasmine 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 hours solving puzzles. She solved 3 sudokus and 6 hanjies.

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

  • A
  • B
  • C
  • D
  • E

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

Q22:

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

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

  • A
  • B
  • C
  • D
  • E

Solve your equation to find .

Q23:

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

Q24:

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

Q25:

Sarah 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?

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