Question

Leona has a jar containing some sweets, of which 90 are pear drops. She takes a random sample of 70 sweets from the jar and finds that 22 of these are pear drops. She then puts the 70 sweets back into the jar. Work out an estimate for the total number of sweets in the jar. Give your answer to the nearest integer.​

Answer 1

We can use the concept of proportion to estimate the total number of sweets in the jar.

Let's represent the total number of sweets in the jar by "x". We know that 90 of these are pear drops. So the proportion of pear drops in the jar is 90/x.

Leona takes a random sample of 70 sweets from the jar and finds that 22 of these are pear drops. So the proportion of pear drops in the sample is 22/70.

We can assume that the proportion of pear drops in the sample is roughly equal to the proportion of pear drops in the jar. Therefore, we can set up a proportion and solve for "x":

90/x = 22/70

Cross-multiplying, we get:

22x = 90 * 70

Dividing both sides by 22, we get:

x = 90 * 70 / 22

Using a calculator, we get:

x ≈ 287

Therefore, an estimate for the total number of sweets in the jar is 287, rounded to the nearest integer.