Question

Paul Linda and Aaron make handmade cards. Paul can make one card for every three cards Linda makes. Linda can make three cards for every two cards that Aaron makes. During a week Aaron makes 72 cards. How many more cards does Linda make those Paul during this week?

Answer 1

Linda makes 3 more cards for every 1 card that Paul makes

Explanation:

Paul can make one card for every three cards Linda makes.

Paul : Linda = 1 : 3

P/L = 1/3

3P = L (1)

Linda can make three cards for every two cards that Aaron makes.

Linda : Aaron = 3 : 2

L/A = 3/2

2L = 3A (2)

During a week Aaron makes 72 cards. How many more cards does Linda make those Paul during this week?

From (2)

L = 3/2A

A = 72

L = 3/2*72

= (3*73) / 3

= 216/2

= 108

Linda = 108

From (1)

P = 1/3L

= 1/3*108

= (1*108) / 3

= 108/3

= 36

Paul = 36

Finally, the number of cards that Linda makes more than Paul is:

Linda : Paul = 108 : 36

= 108/36

= 3/1

Linda : Paul = 3 : 1

Therefore, Linda makes 3 more cards for every 1 card that Paul makes