Question

Ryan and Sarah collect baseball cards. Ryan has 150 baseball cards and collects 10 cards per week. Sarah has 233 baseball cards and collects 5 cards per week. After about how many weeks will Ryan and Sarah have the same number of cards?​

Answer 1

About 17 weeks

Explanation:

Given

Ryan:

`Initial = 150`

`Additional = 10` (weekly)

Sarah:

`Initial = 233`

`Additional = 5` (weekly)

Required

Determine the number of weeks they have the same cards

Represent the number of weeks with w:

For Both individuals, number of card at any given week is:

`Initial + Additional * w`

So,

For Ryan, the expression is:

`150 + 10 * w`

`150 + 10w`

For Sarah, the expression is:

`233 + 5 * w`

`233 + 5 w`

To determine the number of weeks, we have to equate both equations:

`150 + 10w= 233 + 5 w`

Collect Like Terms

`10w - 5w = 233 - 150`

`5w = 83`

Solve for w

`w = 83/5`

`w = 16.6`

16.6 implies about 17 weeks, because 16.6 approximates to 17

Conclusively, Ryan and Sarah will have the same number of balls in about 17 weeks