Answer:

2.

• as the number of hours goes up, the piece of work goes down
• as the number of hours goes down, the piece of work goes up

we can use,

t = k/n

where

• t = number of hours
• k = constant of proportionality
• n = number of piece of work (days)

t = 8

n = 5

8 = k/5

8 × 5 = k/5 × 5

40 = k

k = 40

so now we know:

t = 40/n

and when n = 10

t = 40/10

= 4

how many days could he finish a similar piece of work by working 10 hours a day?

10 = 40/n

n = 40/10

= 4

So, the carpenter needs 4 days to complete the job by working 10 hours a day.

3.

50 = number of books

3 and 2 = terms in the ratio

5 = sum of the terms in the ratio

50 / 5 = 10

then multiply 10 by each of the term in the ratio

10 × 3 = 30 (math books)

10 × 2 = 20 (science books)

Final answer:

30 and 20

to check, add them all

30 + 20 = 50