Marcin buys 7 rulers and 15 crayons for £7 - OCR - GCSE Maths - Question 5 - 2018 - Paper 4
Question 5
Marcin buys 7 rulers and 15 crayons for £7.
A ruler costs 12p more than a crayon.
Find the cost of one crayon.
Worked Solution & Example Answer:Marcin buys 7 rulers and 15 crayons for £7 - OCR - GCSE Maths - Question 5 - 2018 - Paper 4
Step 1
Let the cost of a crayon be c
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Answer
Let the cost of one crayon be denoted by the variable c (in pence). Since a ruler costs 12p more than a crayon, the cost of a ruler can be expressed as c+12.
Step 2
Set up the equation for the total cost
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Answer
The total cost for 7 rulers and 15 crayons is given as £7, which is equivalent to 700 pence. Therefore, the equation can be set up as follows:
7(c+12)+15c=700
Step 3
Simplify the equation
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Answer
Expanding the equation:
7c+84+15c=700
Combine like terms:
22c+84=700
Step 4
Solve for c
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Answer
Subtract 84 from both sides:
22c=700−84
Which simplifies to:
22c=616
Then, divide by 22:
c = rac{616}{22} = 28
Step 5
Final answer
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Answer
Thus, the cost of one crayon is £0.28 or 28 pence.
