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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 d... 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 will divide the total number of sweets made per day by the number of packets produced daily:
[ \text{Mean number of sweets in one packet} = \frac{1.47 \times 10^7}{3.5 \times 10^5} ]
Calculating this gives:
[ \text{Mean} = \frac{1.47}{3.5} \times 10^{(7 - 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 number of sweets made each year, we will multiply the number of sweets made each day by the number of days in a year:
[ \text{Number of sweets per year} = 1.47 \times 10^7 \times 288 ]
Calculating this:
[ \text{Number of sweets per year} = 4.2336 \times 10^9 ]
In standard form, this can be expressed as 4.23 × 10⁹.
Step 3
Calculate the number of sweets made by one machine each hour.
Answer
First, we need to find the total number of sweets made per day by all machines:
[ \text{Total sweets per day} = 1.47 \times 10^7 ]
Next, we divide this by the number of machines, then by the number of hours:
[ \text{Sweets per machine per hour} = \frac{1.47 \times 10^7}{152 \times 15} ]
Calculating:
[ \text{Sweets per machine per hour} = \frac{1.47 \times 10^7}{2280} \approx 6453.95 ]
Rounded to the nearest 10, this gives us 6450.