Max has a jar of sweets.

Question

All of the sweets are either hard or soft.
There are twice as many hard sweets as soft
sweets.
1/5 of the hard sweets are red.
3/10 of the soft sweets are red.
There are 91 red sweets in total.
Work out the number of sweets in the jar.

Answer 1

h = 2s
1/5 h + 3/10 s = 91
2/5 s + 3/10 s = 91
7/10 s = 91
s = 91 * 10/7 = 130
h = 2s = 260
h+s = 390 sweets in all

Answer 2

number of hards ---- h
number of softs ---- s
but h = 2s

reds = (1/5)h + (3/10)s = 91
times 10
2h + 3s = 910
sub in h = 2s
2(2s) + 3s = 910
7s = 910
s = 130 , then h = 260 , for a total of 390