Question

60 identical machines in a factory pack 150 crates of limes per day

between them.
a) Write the ratio of the number of machines to the number of crates
packed per day in the form 1: n.
b) How many crates of limes would 70 of these machines pack per day?
Give any decimals in your answers to 1 d.p.

Answer 1

a) To write the ratio of the number of machines to the number of crates packed per day in the form 1: n, we need to find the number of crates packed per day per machine. We can do this by dividing the total number of crates packed per day by the number of machines:

Number of crates packed per day per machine = 150 crates/day ÷ 60 machines = 2.5 crates/machine/day

Therefore, the ratio of the number of machines to the number of crates packed per day in the form 1: n is 1:2.5 or 2:5.

b) To find out how many crates of limes 70 of these machines would pack per day, we can use the ratio from part (a) to set up a proportion:

1 machine : 2.5 crates/day = 70 machines : x crates/day

Solving for x, we get:

x = (70 machines × 2.5 crates/day) / 1 machine = 175 crates/day

Therefore, 70 of these machines would pack 175 crates of limes per day.

Answer 2

Explanation:

a) The ratio of the number of machines to the number of crates packed per day can be written as:

60 : 150

To simplify this ratio, we can divide both sides by 10:

6 : 15

Finally, we can divide both sides by 3 to get the ratio in the form 1 : n:

1 : 2.5

Therefore, the ratio of the number of machines to the number of crates packed per day is 1 : 2.5.

b) If 60 machines can pack 150 crates per day, then one machine can pack:

150/60 = 2.5 crates per day

So, 70 machines can pack:

70 × 2.5 = 175 crates per day

Therefore, 70 machines can pack 175 crates of limes per day.