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A company makes sweets - OCR - GCSE Maths - Question 5 - 2017 - Paper 1
Question 5
A company makes sweets. The sweets are put into packets. Here are some facts. 1.47 × 10⁷ sweets are made every day 3.5 × 10⁵ packets of sweets are produced every da... show full transcript
Worked Solution & Example Answer:A company makes sweets - OCR - GCSE Maths - Question 5 - 2017 - Paper 1
Step 1
Calculate the mean number of sweets in one packet.
Answer
To find the mean number of sweets in one packet, we first need to divide the total number of sweets made every day by the total number of packets produced every day:
Mean sweets per packet = [ \frac{1.47 \times 10^7}{3.5 \times 10^5} ]
Calculating this: [ \frac{1.47}{3.5} \times \frac{10^7}{10^5} = 0.42 \times 10^2 = 42 ]
Thus, the mean number of sweets in one packet is 42.
Step 2
Calculate the number of sweets made each year.
Answer
To find the total number of sweets made each year, we multiply the number of sweets made each day by the number of days:
[ 1.47 \times 10^7 \text{ sweets/day} \times 288 \text{ days} = 4.23 \times 10^9 ext{ sweets/year} ]
In standard form, that is 4.23 × 10⁹.
Step 3
Calculate the number of sweets made by one machine each hour.
Answer
First, determine the total number of sweets produced by all machines in one day:
Total sweets per day = [1.47 \times 10^7]
With 152 machines operating for 15 hours per day, the number of sweets produced by one machine per hour is:
Total hours of operation for all machines per day = [152 \times 15 = 2280]
Thus, sweets made by one machine per hour: [ \frac{1.47 \times 10^7}{2280} \approx 6453 ]
Rounding to the nearest 10 gives 6450.