Sunil bought a packet of small balls to give to her pupils. If she gives each pupil 3 small balls , she will have 8 small balls left.

If she gives each pupil 4 small balls instead , she will have 1 small ball left.

a. How many pupils did Sunil give ?

b. Find the number of small balls  she bought.

can you guide this problem with both value left

After giving out 3 balls to each pupil, Sunil had 8 balls left.

She started to give out 1 more ball to each pupil so that each had 4 balls.

After giving out (8 – 1) = 7 additional balls, all pupils had 4 balls each and she had 1 ball leftover.

(a) Number of pupils -> 7

(b) Number of balls -> (7 × 4) + 1 = 29

Alternatively,

Number of pupils -> u

Number of balls (1st scenario) -> (u × 3) + 8 = 3u + 8

Number of balls (2nd scenario) -> (u × 4) + 1 = 4u + 1

3u + 8 = 4u + 1

1u = 7

(a) 7 pupils

(b) 3u + 8 = 29 balls

Thx . Can we do the cup cake in alternative method as well ?

Certainly!

Number of guests → u

Number of cup cakes (1st scenario) → (u × 3) + 8 = 3u + 8

Number of cup cakes (2nd scenario) → (u × 6) – 10 = 6u – 10

3u + 8 = 6u – 10

3u = 18

u = 6

Assume no. of guests = Y

No. of cupcakes Mary has = 3Y + 8 = 6Y – 10  

==> 18 = 3Y

==> Y = 6 guests