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Marcin buys 7 rulers and 15 crayons for £7 - OCR - GCSE Maths - Question 25 - 2018 - Paper 1
Question 25
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 25 - 2018 - Paper 1
Step 1
Find the equations from the problem statement
Answer
Let the cost of one crayon be denoted as ( x ) (in pence). Then, the cost of one ruler is ( x + 12 ) pence. The total cost for 7 rulers and 15 crayons can be represented as:
[ 7(x + 12) + 15x = 700 ]
This equation acknowledges that Marcin spends £7, which is equivalent to 700 pence.
Step 2
Solve the equation
Answer
Expanding the equation:
[ 7x + 84 + 15x = 700 ]
Combining terms gives:
[ 22x + 84 = 700 ]
Next, subtract 84 from both sides:
[ 22x = 700 - 84 ]
[ 22x = 616 ]
Now, divide both sides by 22:
[ x = \frac{616}{22} ]
Thus, ( x = 28 ), meaning the cost of one crayon is 28 pence.