Kelly has 4x as much money as Joey. After Kelly uses some money to buy a racquet, and Joey uses $30 to buy shorts, Kelly has twice as much money as Joey. If Joey started with $98, how much money does Kelly have? what does the racquet cost?

Question

Zoe Adams · Accepted Answer

Kelley has #$136# and racquet costs #$256# As Joey started with #$98# and Kelly had #4# times as much money as Joey had, Kelly started with #98xx4=$392# Assume that racquet costs #$x#, so Kelly will be left with #$392-$x=$(392-x)#. As Joey spent #$30# to buy shorts, he was left with #$98-$30=$68#. Now Kelley has #$(392-x)# and Joey has #68#, as Kelly has twice as much money as Joey has, we have #392-x=2xx68# or #392-x=136# or #392-x+x=136+x# or #136+x=392# or #x=392-136=256# So Kelley has #$136# and racquet costs #$256#

Gabriel Agustin · Answer

undefined Let's represent the amount of money Kelly has as 4x and the amount Joey has as x. According to the information given, after Joey spends $30 on shorts, he has $98 - $30 = $68 left. And after Kelly buys the racquet, she has 4x - r, where r represents the cost of the racquet. We also know that after these expenses, Kelly has twice as much money as Joey, so we can set up the equation: 4x - r = 2(68).

Given that Joey started with $98, we can find the value of x by subtracting the amount he spent on shorts: x = $98 - $30 = $68.

Substituting the value of x into the equation, we have: 4(68) - r = 2(68). Solving for r:

4(68) - r = 2(68)
272 - r = 136
r = 272 - 136
r = $136

Now, we can find the amount of money Kelly has by substituting the value of x into the expression for Kelly's money: Kelly's money = 4(68) = $272. Therefore, Kelly has $272, and the racquet costs $136.