GCSE OCR Maths Ratio: In a box of mixed nuts, the tota

In a box of mixed nuts, the total number of almonds, cashews and peanuts is 1025 - OCR - GCSE Maths - Question 6 - 2018 - Paper 6

Question 6

In a box of mixed nuts, the total number of almonds, cashews and peanuts is 1025. The ratio of almonds to cashews is 1 : 3. The ratio of cashews to peanuts is 5 : 7.... show full transcript

Worked Solution & Example Answer:In a box of mixed nuts, the total number of almonds, cashews and peanuts is 1025 - OCR - GCSE Maths - Question 6 - 2018 - Paper 6

Step 1

Calculate the total parts based on the ratios

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Answer

First, define the variables for each type of nut based on the ratios:

Let the number of almonds be represented as A.
Let the number of cashews be represented as C.
Let the number of peanuts be represented as P.

According to the problem:

The ratio of almonds to cashews is 1:3, so we can express this as: $A = \frac{1}{3}C$ or equivalently, $C = 3A$
The ratio of cashews to peanuts is 5:7, meaning: $C = \frac{5}{7}P$ which can also be written as: $P = \frac{7}{5}C$

Next, the sum of all parts combined equals 1025: $A + C + P = 1025$ .

Step 2

Substitute C and P in terms of A

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Answer

Substituting the expressions for C and P derived earlier into the total: $A + C + P = A + 3A + \frac{7}{5}(3A) = 1025$ This simplifies to: $A + 3A + \frac{21}{5}A = 1025$ Combining terms gives: $\left(1 + 3 + \frac{21}{5}\right)A = 1025$ $\left(\frac{5}{5} + \frac{15}{5} + \frac{21}{5}\right)A = 1025$ $\frac{41}{5}A = 1025$

Step 3

Solve for A

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Answer

Solving for A, we multiply both sides by 5: $41A = 1025 \times 5$ $41A = 5125$ Now dividing both sides by 41 yields: $A = \frac{5125}{41} = 125$ .

Step 4

Calculate Cashews (C)

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Answer

Having the value of A, substitute back to find C: $C = 3A = 3 \times 125 = 375.$ Thus, the number of cashews in the box is 375.

In a box of mixed nuts, the total number of almonds, cashews and peanuts is 1025 - OCR - GCSE Maths - Question 6 - 2018 - Paper 6

Worked Solution & Example Answer:In a box of mixed nuts, the total number of almonds, cashews and peanuts is 1025 - OCR - GCSE Maths - Question 6 - 2018 - Paper 6

Calculate the total parts based on the ratios

Substitute C and P in terms of A

Solve for A

Calculate Cashews (C)

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