Question

Mrs Lim packs 35 big and small bags of candies for her pupils. Each big bag contains 12 candies and each small bag contains 7 candies. The bags contain 300 candies altogether. How many big bags of candies and how many small bags of candies does she pack?

Answer 1

there are 11 big-bags and 24 small-bags.

Explanation:

there are x big-bags and y small-bags.

so now we can know:

(1) x + y = 35

(2) 12x + 7y = 300

in (1),we can do like this:

both left and right x7

then (x + y)x7 = 35 x 7

then 7x + 7y = 35 x 7

then 7x + 7y = 245

now,

(1)7x + 7y =245

(2)12x + 7y = 300

we can both left and right do this: (2) - (1)

then

(12x + 7y) - (7x + 7y) = 300 -245

then

12x + 7y - 7x - 7y = 300 -245

then

12x - 7x +7y - 7y =300 -245

then

5x =55

then

5x ÷ 5 = 55 ÷ 5

then

x = 11

because

x + y =35;x=11

so

11 + y =35

11+ y -11 = 35 -11

then

y = 24

now we know:there are 11 big-bags and 24 small-bags.