Worksheet: Solving Proportions Using Equivalent Expressions and Unit Rates

In this worksheet, we will practice solving proportion problems using equivalent ratios and unit rates and practice using this to solve problems in real-life situations.

Q1:

If 1 . 2 ๐‘Ž = 1 . 5 5 3 . 1 , then find the value of ๐‘Ž .

Q2:

If 7 out of 28 students go to bed before 10 pm, then how many go to bed before 10 pm in a school of 1,100 students?

Q3:

Fadyโ€™s car can travel 570 miles on 15 gallons of gasoline. Using a ratio table, determine how many miles he can travel on 11 gallons.

Q4:

Mariam sliced 4 pineapples in 16 minutes at a fruit fair. Determine how many pineapples Mariam can slice in 36 minutes at this rate.

Q5:

Yasmine earned $87.12 in a week for working 18 hours. If she works 25 hours the following week, determine the amount of money she will earn.

Q6:

A shop received a shipment of 200 keyboards at a price of $7โ€Žโ€‰โ€Ž000. If the shop gave away 9 of them, use a ratio table to find how much money it lost.

  • A$35
  • B$31
  • C$350
  • D$315
  • E$180

Q7:

A dolphin dove 354 feet in 3 1 2 minutes. Given there are 3 feet in a yard, determine how many yards the dolphin dove, and then, by using a table, determine an algebraic expression that relates the number of feet ๐‘› to the number of yards.

  • A 101 yd, ๐‘› รท 3 1 2 .
  • B 35 yd, 3 + ๐‘› .
  • C 54 yd, ๐‘› รท 6 1 2 .
  • D 118 yd, ๐‘› รท 3 .
  • E 708 yd, 6 + ๐‘› .

Q8:

Adham has $200 and wants to purchase some DVDs that cost $20 each. He claims that the amount of money remaining after his purchase will be proportional to the number of DVDs he decides to buy. Is his claim valid?

  • A no
  • B yes

Q9:

At a farmersโ€™ market, the seller uses the equation ๐‘ = 2 . 5 0 ร— ๐‘ค to calculate the cost (in dollars) for ๐‘ค kg of apples. What is the unit rate?

Q10:

A car consumes 10 liters of fuel to travel 125 km. At the same rate of fuel consumption, how many litres of fuel are needed to travel 187.5 km and how far can it travel using 12 liters of fuel?

  • Afuel = 1 6 L , the distance = 1 5 0 k m
  • Bfuel = 1 5 L , the distance = 1 , 5 0 0 k m
  • Cfuel = 1 , 5 0 0 L , the distance = 1 6 k m
  • Dfuel = 1 5 L , the distance = 1 5 0 k m

Q11:

If 7 pounds of meat cost $42, how much do 5 pounds of meat cost?

Q12:

Maher can paint 3 portraits in 6 hours. At this rate, how many portraits can Victor paint in 36 hours?

Q13:

Dalia cycles with a constant rate of 14 miles per hour. Which of the following tables represents this?

  • A
    Time (Hours) 14 28 42 56
    Distance (Miles) 1 2 3 4
  • B
    Time (Hours) 1 2 3 4
    Distance (Miles) 14 14 14 14
  • C
    Time (Hours) 1 2 3 3
    Distance (Miles) 0 14 28 42
  • D
    Time (Hours) 1 2 3 4
    Distance (Miles) 14 28 42 56
  • E
    Time (Hours) 0 14 28 42
    Distance (Miles) 1 2 3 4

Q14:

If the price of 6 pens is 12 LE, what is the price of 3 pens?

Q15:

A shop sells 60 stickers for $3. Select the correct statement from the following

  • AThree stickers cost 60 cents.
  • BFor $1, you can buy 40 stickers.
  • CSeven stickers cost 60 cents.
  • DFor $2, you can buy 40 stickers.
  • EFor $1, you can buy 30 stickers.

Q16:

Raghda can read 80 pages of a novel in 4 hours. At this rate, how many pages of a novel can Raghda read in 15 hours?

Q17:

A candy shop can make 7 ice cream cakes in 3 hours. At this rate, how many ice cream cakes can the shop make in 9 hours?

Q18:

It takes 5 days to vaccinate 245 children, where the same number of children are vaccinated each day. How many children can be vaccinated in 6 days?

Q19:

Bassem read 300 pages in 30 days. How many pages will he read in 5 days if he reads at the same rate?

Q20:

The table shows the distance a cyclist traveled. If she continued to cycle at the same rate, determine the distance she will have traveled after four minutes.

Time (min) 1 2 3 4
Distance (yd) 350 700 1,050 ?

Q21:

The price of 5 litres of liquid soap is 66.5 LE. At the same cost/litre, how much would 20 litres of the same liquid soap cost, and how many litres would cost 159.6 LE?

  • A266 LE, 13 L
  • B 1,330 LE, 12 L
  • C 1,330 LE, 13 L
  • D266 LE, 12 L

Q22:

A customer service agent can handle 7 calls in 21 minutes. How many calls can this agent handle in 30 minutes?

Q23:

If water flows through a pipe at a rate of 1 3 1 2 litres per minute, how many minutes does it take to fill three 5-litre containers?

  • A 2
  • B 1 0 2 7
  • C 1 5 1 4
  • D 1 0 9

Q24:

It takes a mathematics teacher 35 minutes, or of an hour, to mark the tests of one-third of their class.

What fraction of the classโ€™s tests could they mark in five minutes?

  • A
  • B
  • C
  • D
  • E

What fraction of the classโ€™s tests could they mark in an hour? Simplify the answer.

  • A
  • B
  • C
  • D
  • E

How long would it take them to mark all the tests? Express your answer in hours and minutes.

  • A 1 hour
  • B 1 hour 5 minutes
  • C 1 hour 45 minutes
  • D 1 hour 9 minutes
  • E 1 hour 50 minutes

Q25:

Which of the following is equal to 5 . 2 9 . 1 ?

  • A 1 4 8
  • B 8 1 1
  • C 2 1 8
  • D 8 1 4

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