Question

sonji paid $25 for two scarves, which were different prices. when she got home she could not find the receipt. she remembered that one scarf cost $3 more than the other. what was the price of the more expensive scarf?
○ $11
○ $12
○ $13
○ $14

Explanation:

Step1: Define variables

Let the price of the less expensive scarf be $x$. Then the price of the more expensive scarf is $x + 3$.

Step2: Set up equation

The total cost of the two scarves is $25$, so we have the equation $x+(x + 3)=25$.

Step3: Solve the equation

Simplify the left side: $2x+3 = 25$. Subtract 3 from both sides: $2x=25 - 3=22$. Divide both sides by 2: $x = 11$.

Step4: Find the price of the more expensive scarf

The more expensive scarf is $x + 3=11 + 3 = 14$? Wait, no, wait. Wait, let's check again. Wait, if we test the options:

• Option A: $11$. Then the other is $11 - 3 = 8$. $11+8 = 19

eq25$.

• Option B: $12$. Then the other is $12 - 3 = 9$. $12 + 9=21

eq25$.

• Option C: $13$. Then the other is $13 - 3 = 10$. $13+10 = 23

eq25$.

• Option D: $14$. Then the other is $14 - 3 = 11$. $14+11 = 25$. Ah, there we go. So my earlier algebra had a mistake. Let's do it correctly. Let the more expensive be $y$, less be $y - 3$. Then $y+(y - 3)=25$. So $2y-3 = 25$. $2y=28$. $y = 14$? Wait, no, $25 + 3=28$, $28/2 = 14$. Wait, but the options have $14$? Wait, the options are $11,12,13,14$. Wait, when I did $x+(x + 3)=25$, $2x=22$, $x = 11$, so the more expensive is $14$? But $11 + 14=25$, and $14 - 11=3$. So yes, the more expensive is $14$? Wait, but let's check the options again. Wait, maybe I misread the options. Wait, the options are $11,12,13,14$. So the correct one is $14$? Wait, but let's check: if the more expensive is $14$, the less is $11$, $14 + 11=25$, and $14 - 11=3$. Correct. So the answer is $14$.

Answer:

D. $14$