joe wants to spend 70. dollars at most and has 60 cu inches of space left in his soldier's care package. candy costs $7 and takes up 3 cu inch of space phone cards cost $5. and take up 15 cu in. of space.

Is this correct? if not please change it or tell me how ??? thanks ann

1. write a system of 4 inequalities that model his possible purchases.
Let x = # of candy and y = # of phone cards.
I wrote 7x + 5y <= 70
3x + 15y <= 60
x<= 10 (limited money 10 x $7 <= 70)
y <= 4
limited space (4 x 15 cu in < = 60)

The inequalities you wrote are mostly correct, but there is a minor error in the last inequality for limited space.

1. The cost inequality is correct: 7x + 5y <= 70 (since Joe wants to spend at most $70)
2. The space inequality is correct: 3x + 15y <= 60 (since Joe has 60 cu inches of space left)

However, the inequality for limited candy purchases (x <= 10) is unnecessary since it is already accounted for in the cost inequality (7x + 5y <= 70).

The last inequality for limited phone card purchases should be y <= 4, as you correctly mentioned (since Joe wants to spend at most $70 and each phone card costs $5).

So the correct system of inequalities to model Joe's possible purchases is:
7x + 5y <= 70 (cost)
3x + 15y <= 60 (space)
y <= 4 (phone cards)