Question

There are two ways of scoring points in a ball game: a ‘major’ scores 5 points and a ‘minor’
scores 3 points.
In a match played yesterday, the Reds beat the Blues 77–52 despite the fact that the Blues
scored exactly twice as many majors as minors, whilst the Reds scored exactly half as many
majors as minors.
How many majors were scored altogether in yesterday’s match?
Hi, how do I do this? Thank you so much in advance!

Answer 1

r = Reds' majors , b = Blues' majors

Blues ... 5 b + (3 b / 2) = 52
... 10 b + 3 b = 104
... b = ?

Reds ... 5 r + (3 * 2 * r) = 77
... 5 r + 6 r = 77
... r = ?

r + b = ?

Answer 2

If the Reds scored x majors and y minors,
5x+3y = 77
y = 2x
So, x=7, y=14

If the Blues scored x majors and y minors, then
5x+3y = 52
x = 2y
y=4, x=8

7+8 = 15
also, 14+4=18, and 5*15 + 3*18 = 77+52