# 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?

Kelley has

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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.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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