Question

a store sells white scarves and red scarves.

• a white scarf costs $3.
• a red scarf costs $5.

on monday, the store sold 12 scarves for a total of $50.
what is the total number of red scarves that the store sold on monday?
a. 4
b. 5
c. 6
d. 7

Explanation:

Step1: Define variables

Let \( x \) be the number of white scarves and \( y \) be the number of red scarves. We know two equations: \( x + y = 12 \) (total number of scarves) and \( 3x + 5y = 50 \) (total cost).

Step2: Solve the first equation for \( x \)

From \( x + y = 12 \), we get \( x = 12 - y \).

Step3: Substitute \( x \) into the second equation

Substitute \( x = 12 - y \) into \( 3x + 5y = 50 \):
\( 3(12 - y) + 5y = 50 \)
\( 36 - 3y + 5y = 50 \)
\( 36 + 2y = 50 \)

Step4: Solve for \( y \)

Subtract 36 from both sides: \( 2y = 50 - 36 = 14 \)
Divide by 2: \( y = \frac{14}{2} = 7 \)? Wait, no, wait. Wait, let's check again. Wait, 3(12 - y) is 36 - 3y, plus 5y is 36 + 2y. 50 - 36 is 14, so 2y =14, y=7? But wait, let's check the total number. If y=7, then x=12-7=5. Then total cost is 35 +57=15 +35=50. Yes, that works. Wait, but the options are A.4, B.5, C.6, D.7. So D is 7. Wait, but let me check again. Wait, maybe I made a mistake? Wait, no, the calculation is correct. 35=15, 5*7=35, 15+35=50. And 5+7=12. So the number of red scarves is 7. Wait, but the options have D as 7. So the answer is D? Wait, but let me check the problem again. Wait, the problem says "What is the total number of red scarves that the store sold on Monday?" So according to the calculation, it's 7. So the answer is D.7.

Wait, but maybe I messed up the variables. Let me redefine: Let y be red scarves, x be white. So x + y =12, 3x +5y=50. Solve for y. x=12 - y. Substitute into 3x +5y=50: 3(12 - y) +5y=50 → 36 -3y +5y=50 → 36 +2y=50 → 2y=14 → y=7. Yes, that's correct. So the number of red scarves is 7, which is option D.

Answer:

D. 7