Let's turn this problem into a system of equations!
Let s = cost of one scarf
Let h = cost of one hat
What's given:
4s+6h=52
2h=1+s
You can either use subtraction or substitution. Let's do substitution.
In the second equation, we can isolate the s on one side.
s=2h-1
Then we can plug this value into the first equation.
4(2h-1)+6h=52
(Use PEMDAS to solve!:))
8h-4+6h=52
14h=56
h=4
This means hats cost $4.
Now that we know how much hats cost, let's plug that back into one of the given equations.
2h=1+s
2(4)=1+s
8=1+s
7=s
This means that scarves cost $7.
To confirm our answer is correct, let's plug the answers we found into the other given equation.
4s+6h=52
4(7)+6(4)=52
28+24=52
52=52
Yep! Now we know it's the right answer.
ANSWER: Scarves cost $7, hats cost $4.
