Answer:
Hat costs $17.5
Step-by-step explanation:
Let x represent the cost of one sweater.
Let y represent the cost of one hat.
James spent 4/5 of his birthday money on three sweaters and four hats. This means that she spent 4/5 of his birthday money on 3x +4y
Each sweater cost twice as much as each hat. It means that
x = 2y
Assuming his total birthday money was $z and after spending 4/5 of it on the hats and sweaters, he had $35 left after his shopping spree, then,
z - 4z/5 = 35
Cross multiplying by 5
5z - 4z = 175
z = 175
This means that his birthday money was $175
It means that
3x + 4y = 175 - - - - - - - -1
Substituting x = 2y into equation 1, it becomes
3(2y) + 4y = 175
6x + 4y = 175
10y = 175
x = 175/10= 17.5
x = 2y = 17.5×2 = $35
