Question

Sweets are sold in small packs and in big packs.

There is a total of 175 sweets in 4 small packs and 3 big packs.
There is a total of 154 sweets in 5 small packs and 2 big packs.
Work out the number of sweets in each small pack and in each big pack.

Answer 1

Explanation:

Let x - be the number of sweets in small packs

y - be the number of sweets in big packs

Therefore, we have:

4x + 3y = 175 (1)

5x + 2y = 154 (2)

Now, we find the difference between (1) & (2) is:

y-x = 21. Thus, y = 21+x

Now we substitute the value of y = 21+x to any of the two statements, we have 4x + 3(21+x) = 175 => 4x + 63 + 3x = 175.

Hence, 7x = 175 - 63 = 112 or simply, x=16.

Now, finding the value of y:

5(16) + 2y = 154

80 + 2y = 154

2y = 154-80

2y = 74

y = 37.

Therefore, there are 16 sweets in each small pack and 37 sweets in each big pack.