Ratio problem solving Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Ratio problem solving questions. See exactly how to solve problems on recipe scaling, unitary method, scale factor, unit price.

recipe scalingunitary methodscale factorunit pricecurrency conversionmultiplying by a rate
GCSE Foundation70 questionsStep-by-step solutions
Question 1
2 markseasy
A recipe for 44 people uses 200200 g of flour. How much flour is needed for 66 people?

Worked solution

  1. Find the amount for one person

    200÷4=50 g200 \div 4 = 50 \text{ g}

    Divide the flour by the number of people to get the amount per person.

  2. Scale up to six people

    50×6=300 g50 \times 6 = 300 \text{ g}

    Multiply the amount for one person by 66.

  3. State the answer

    300 g300 \text{ g}

    The recipe needs 300300 g of flour for 66 people.

Answer
300 g300 \text{ g}
Question 2
2 markseasy
A recipe makes 1212 biscuits using 150150 g of butter. How much butter is needed to make 1818 biscuits?

Worked solution

  1. Find the scale factor

    18÷12=1.518 \div 12 = 1.5

    The new batch is 1.51.5 times the size of the original.

  2. Scale the butter

    150×1.5=225 g150 \times 1.5 = 225 \text{ g}

    Multiply the butter by the same scale factor.

  3. State the answer

    225 g225 \text{ g}

    1818 biscuits need 225225 g of butter.

Answer
225 g225 \text{ g}
Question 3
2 markseasy
Three identical pens cost £1.35. Work out the cost of seven of these pens.

Worked solution

  1. Find the cost of one pen

    1.35÷3=0.451.35 \div 3 = 0.45

    Divide the total by 33: one pen costs 4545p.

  2. Find the cost of seven pens

    0.45×7=3.150.45 \times 7 = 3.15

    Multiply the price of one pen by 77.

  3. State the answer

    £3.15\pounds 3.15

    Seven pens cost £3.15.

Answer
£3.15\pounds 3.15
Question 4
1 markeasy
The exchange rate is 11 pound =1.15= 1.15 euros. Change £40 into euros.

Worked solution

  1. Choose the operation

    pounds×1.15=euros\text{pounds} \times 1.15 = \text{euros}

    Each pound is worth 1.151.15 euros, so multiply by the rate.

  2. Multiply

    40×1.15=4640 \times 1.15 = 46

    40×1.15=4640 \times 1.15 = 46.

  3. State the answer

    46 euros46 \text{ euros}

    £40 is worth 4646 euros.

Answer
46 euros46 \text{ euros}
Question 5
2 markseasy
The exchange rate is 11 pound =1.15= 1.15 euros. Change 9292 euros into pounds.

Worked solution

  1. Choose the operation

    euros÷1.15=pounds\text{euros} \div 1.15 = \text{pounds}

    Going back from euros to pounds is the inverse, so divide by the rate.

  2. Divide

    92÷1.15=8092 \div 1.15 = 80

    92÷1.15=8092 \div 1.15 = 80.

  3. State the answer

    £80\pounds 80

    9292 euros is worth £80.

Answer
£80\pounds 80

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