Bailey has $105. She spends 3/7 on a new jacket and 1/5 on a new sweater. How much money does she have left?
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To find out how much money Bailey has left, we need to subtract the amounts she spent on the new jacket and sweater from her initial amount of $105.
First, let's calculate the amount Bailey spent on the new jacket. We know that she spent 3/7 of her money on the jacket. To do this, we multiply 3/7 by $105:
Amount spent on the jacket = (3/7) * $105
To simplify this calculation, we can divide the numerator (3) by the denominator (7) and then multiply by $105:
Amount spent on the jacket = (3/7) * $105 = ($15 * 3)/7 = $45/7
Next, let's calculate the amount Bailey spent on the new sweater. We're given that she spent 1/5 of her money on the sweater. So, we multiply 1/5 by $105:
Amount spent on the sweater = (1/5) * $105
Again, to simplify this calculation, we divide the numerator (1) by the denominator (5) and then multiply by $105:
Amount spent on the sweater = (1/5) * $105 = ($21 * 1)/5 = $21/5
Now, we can add the amount spent on the jacket and the amount spent on the sweater to find the total amount Bailey spent:
Total amount spent = Amount spent on the jacket + Amount spent on the sweater
Total amount spent = $45/7 + $21/5
To add these fractions, we need a common denominator. The common denominator for 7 and 5 is 35:
Total amount spent = ($45 * 5)/(7 * 5) + ($21 * 7)/(5 * 7)
Total amount spent = $225/35 + $147/35
Now that the fractions have the same denominator, we can add them:
Total amount spent = ($225 + $147)/35
Total amount spent = $372/35
Finally, we can subtract the total amount spent from Bailey's initial amount to find out how much money she has left:
Money remaining = Initial amount - Total amount spent
Money remaining = $105 - $372/35
To subtract the fractions, we need a common denominator. The common denominator for 35 and 1 is also 35:
Money remaining = $105/1 - ($372 * 1)/(35 * 1)
Money remaining = $105/1 - $372/35
Now that the fractions have the same denominator, we can subtract them:
Money remaining = ($105 * 35 - $372)/35
Money remaining = $3675 - $372
Money remaining = $3303
Therefore, Bailey has $3303 left.
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I've shown you how to do the last couple of problems. Now it's your turn.
I'll be glad to check your answer.