Aset of children’s blocks contains 3 shapes: longs, flats, and cubes. there are 3 times as many longs as cubes, and 30 fewer flats than longs. if there are 600 blocks in all, how many long’s are there?

There are 126 longs

Step-by-step explanation:

Let's represent the number of longs by l, number of flats by f and number of cubes by c.

We are told that there are 600 blocks in all.

This implies l + f + c = 600

We also know that there are 3 times as many longs as cubes: this mean

c = 3l

There are also 30 fewer flats than longs.

This mean f + 30 = l I.e f = l - 30

We now have 3 equations to solve simultaneously

l + f + c = 600 (i)

c = 3l(ii)

l -30 = f(iii)

We can substitute equations iii and ii into I

l + l - 30 + 3l = 600

5l - 30 = 600

5l = 630

l = 630/5 = 126.