(31)
let x and y be the 2 numbers, x > y, then
x + y = 12 and
x - y = 4
add the 2 equations term by term
2x = 16 ( divide both sides by 2 )
x = 8
substitute x = 8 into x + y = 12
8 + y = 12 ⇔ y = 12 - 8 = 4
the 2 numbers are 8 and 4
(32)
let the 2 numbers be x and y, x > y, then
x - y = 3 and
x + y = 13
add the 2 equations term by term
2x = 16 ( divide both sides by 2 )
x = 8
substitute x = 8 into x + y = 13
8 + y = 13 ⇒ y = 13 - 8 = 5
the 2 numbers are 8 and 5
(33)
let s be the cost of senior citizen ticket and c be the cost of a child ticket, then
3s + c = 38 → (1)
3s + 2c = 52 → (2)
subtract (1) from (2) term by term
c = 14
substitute c = 14 into (1)
3s + 14 = 38 ( subtract 14 from both sides )
3s = 24 ( divide both sides by 3 )
s = 8
the cost of a senior citizen ticket is $8 and a child ticket is $14