Question

The number of new bicycles must be more than 13 times the number of new treadmills. Each bicycle costs $340 and each treadmill costs $670. He must spend less than $5,650. Select all of the constraints for this situation. a) y>13x b)340x+670y≤5650 c)y>0 340x+670y<5650 d) x>13y x>0

Answer 1

Answer: c.
`y>0\ ;\ 340x+670y<5650`

d.
`x>13y ; x>0`

Explanation:

Let x be the number of new bicycles and y be the number of new treadmills.

Given : The number of new bicycles must be more than 13 times the number of new treadmills.

i.e.
`x>13y`

Each bicycle costs $340 and each treadmill costs $670.

He must spend less than $5,650.

i.e.
`340x+670y<5650`'

Hence, the constraints for this situation will be :

`x>13y ; x>0`

`340x+670y<5650`

Hence, c and d are the correct options.

Answer 2

c and d

Explanation:

The cost inequalities tell you that x corresponds to bicycles, so answer (a) is incorrect. The cost constraint is strictly less than, so answer (b) is incorrect.

(c) correctly expresses the cost constraint.

(d) correctly expresses the relationship between bicycles (x) and treadmills (y).

_____

The only integer solution is y=0 and 0 < x ≤ 15.