# Worksheet: Applications of Multistep Equations

In this worksheet, we will practice writing and solving multistep word-problem equations.

Q1:

Given that , find the value of .

Q2:

If , what is the value of ?

Q3:

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

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

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 minutes
• B minutes
• C minutes
• D minutes
• E 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 , the distance traveled.

• A
• B
• C
• D
• E

Q11:

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

• A in2
• B in2
• C in2
• D in2
• E 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 represent the number.

• A
• B
• C
• D
• E

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

• A29 weeks, \$40
• B7 weeks, \$18
• C14 weeks, \$18
• D14 weeks, \$25
• E7 weeks, \$25

Q17:

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

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

• A
• B
• C
• D
• E

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 12.10 miles
• B 6.05 miles
• C 7.6 miles
• D 3.8 miles
• E 19 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 for 15 minutes per pound plus an additional 30 minutes.

A joint of beef takes hours to roast at .

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 represent the number.

• A
• B
• C
• D
• E

Q24:

Let represent an unknown number. Write an equation that represents the statement βForty less than three times an unknown number is twenty.β

• A
• B
• C
• D
• E

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?