Question

tori was shopping for a new dress for her schools spring dance. she spent $40 on the dress she picked, but she had expected to spend 50% more than that. how much had tori expected to spend? $\square$ submit

Explanation:

Step1: Understand the relationship

Let the expected amount be $x$. She spent 50% more than expected, so the amount spent is $x + 0.5x = 1.5x$. We know she spent $40, so we set up the equation $1.5x = 40$.

Step2: Solve for x

To find $x$, we divide both sides of the equation by 1.5: $x=\frac{40}{1.5}=\frac{40\times2}{3}=\frac{80}{3}\approx26.67$? Wait, no, wait. Wait, no, the problem says "she spent $40, but she had expected to spend 50% more than that". Wait, no, wait, maybe I misread. Wait, "she spent $40 on the dress she picked, but she had expected to spend 50% more than that". Wait, so expected is 50% more than spent? Wait, no, "expected to spend 50% more than that" – "that" is the amount she spent? Wait, no, maybe the other way. Wait, no, let's re-express. Let me re-express: Let expected amount be $E$. She spent $40, and she had expected to spend 50% more than what she spent? Wait, no, the wording: "She spent $40 on the dress she picked, but she had expected to spend 50% more than that." So "that" is the amount she spent? Wait, no, that can't be. Wait, maybe "that" is the expected? No, no. Wait, maybe I got it reversed. Wait, maybe: She spent $40, which is less than what she expected. She expected to spend 50% more than what she spent. Wait, no, the problem says "she had expected to spend 50% more than that" – "that" is the $40? Wait, no, that would mean expected is 40 + 0.540 = 60? Wait, no, wait, let's read again: "She spent $40 on the dress she picked, but she had expected to spend 50% more than that. How much had Tori expected to spend?" So "that" is the amount she spent, which is $40. So expected is 50% more than $40. So 40 + 0.5*40 = 40 + 20 = 60? Wait, but that seems the opposite. Wait, no, maybe I misread. Wait, maybe "she spent $40, but she had expected to spend 50% more than that" – so expected is 50% more than the amount she spent. So expected = 40 + 0.540 = 60. Wait, but let's check the equation. Let me define: Let $E$ be the expected amount. She spent $40, and $40 is less than $E$, and $E$ is 50% more than $40. So $E = 40 + 0.540 = 401.5 = 60. Wait, that makes sense. So my initial mistake was reversing. So the correct equation is: Expected amount $E = 40 + 0.5*40 = 40*1.5 = 60$. Wait, but let's do it with algebra. Let $E$ be expected. She spent $40, and $E = 40 + 0.540$? No, wait, "expected to spend 50% more than that" – "that" is the amount she spent, which is $40. So 50% more than 40 is 40(1 + 0.5) = 40*1.5 = 60. So the expected amount is $60.

Answer:

60