Question

Dakota bought 2 scarves and 1 hat for $13. Kristina bought 1 scarf and two hats for $14. What was the price for one hat and one scarf?

Answer 1

Answer:

The price for one hat was $5 and the price for one scarf was $4

Step-by-step explanation:

Let

x ----> the price for one scarf in dollars

y ----> the price for one hat in dollars

we know that

Dakota bought 2 scarves and 1 hat for $13

so

$2x+y=13$ ----> equation A

Kristina bought 1 scarf and two hats for $14

so

$x+2y=14$ ----> equation B

Solve the system by elimination

Multiply by -2 both sides equation B

$-2(x+2y)=-2(14)$

$-2x-4y=-28$ ----> equation C

Adds equation A and equation C

$2x+y=13\\-2x-4y=-28\\---------\\y-4y=13-28\\-3y=-15\\y=5$

Find the value of x

substitute the value of y in any equation

equation B

$x+2(5)=14\\x=14-10\\x=4$

therefore

The price for one hat was $5 and the price for one scarf was $4