AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
Ashley spent of her money and an additional on a concert ticket. She then spent of the remaining money and an additional on a dress. If she had left, how much money did she have at first?
Full solution
Q. Ashley spent of her money and an additional on a concert ticket. She then spent of the remaining money and an additional on a dress. If she had left, how much money did she have at first?
- Initial Amount Calculation: Let's denote Ashley's initial amount of money as . According to the problem, she spent of her money and an additional on a concert ticket. The amount spent on the concert ticket can be represented as .
- Concert Ticket Expense: After buying the concert ticket, Ashley is left with of her initial money, which is . Then she spent of the remaining money and an additional on a dress. The amount spent on the dress can be represented as .
- Dress Purchase: The remaining money after buying the dress is of the money she had after buying the concert ticket, which is . So, the equation representing the remaining money after all spending is:\(0\).\(75\) \times \(0\).\(70\)X - (\$)\(24\) = (\$)\(282\).
- Equation Setup: Now, let's solve the equation for \(X\). First, we simplify the left side of the equation:\(\newline\)\(0.75 \times 0.70X - (\$)24 = (\$)282\)\(\newline\)\(0.525X - (\$)24 = (\$)282\)
- Simplify Equation: Next, we add \(\$24\) to both sides of the equation to isolate the term with X on one side:\(\newline\)\(0.525X - \$24 + \$24 = \$282 + \$24\)\(\newline\)\(0.525X = \$306\)
- Isolate X: Now, we divide both sides of the equation by \(0.525\) to solve for \(X\): \(\newline\)\[\frac{0.525X}{0.525} = \frac{\$(306)}{0.525}\]\(\newline\)X = \$(\(582\).\(8571\))
- Final Calculation: Since the amount of money should be a whole number, we round the value of \(X\) to the nearest dollar. Therefore, Ashley had \(\$583\) at first.
