Question

A seamstress gets an order to make some skirts.

If she takes it easy and makes 3 skirts a day she’ll finish on Sunday.

If she works really hard and makes 5 skirts a day, she’ll finish on Friday.

What day is it today?

(need to show working out)

Answer 1

Tuesday

Explanation:

Let the days of the week be numbered 1–7, starting with Monday and ending with Sunday. Let t represent today. We can equate the number of skirts finished by Friday (day 5) with the ones finished by Sunday (day 7) at the lower rate. (days × (skirts/day) = skirts)

... (5-t)×5 = (7-t)×3

... 25 -5t = 21 -3t . . . . . eliminate parentheses

... 4 = 2t . . . . . . . . . . . . add 5t-21

... 2 = t . . . . . . . . . . . . . divide by 2

Day 2 corresponds to Tuesday.

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Check solution

(5-2)·5 = 15 = (7-2)·3 skirts are being made.