The cost of 4 scarves and 6 hats is $52. The cost of two hats is $1 more than the cost of one scarf. What are the costs of one scarf and one hat?
Please show me how to set this up and work it.
4s+6h = 52
2h = 1+1s
so, now we know that
6h = 3+3s, so
4s+6h = 4s + 3+3s = 7s+3, and
7s+3=52
7s=49
s=7
so, 2h=1+s = 1+7 = 8, and
h=4
Thank you! It did work very well. I will use this website more frequently.
Where did the 6h=3+3s come from? Not very good at algebra
To solve this problem, let's assign variables to the unknown quantities. Let's say the cost of one scarf is "x" dollars, and the cost of one hat is "y" dollars.
According to the problem, the cost of 4 scarves and 6 hats is $52. We can write this as an equation:
4x + 6y = 52 ---(Equation 1)
The problem also states that the cost of two hats is $1 more than the cost of one scarf. We can write this as another equation:
2y = x + 1 ---(Equation 2)
Now we have two equations with two variables. We can solve this system of equations using substitution or elimination.
Let's use substitution to solve this system.
Step 1: Solve Equation 2 for x.
x = 2y - 1
Step 2: Substitute x into Equation 1.
4(2y - 1) + 6y = 52
Step 3: Solve the equation.
8y - 4 + 6y = 52
14y - 4 = 52
14y = 56
y = 4
Step 4: Substitute y = 4 into Equation 2 to find x.
x = 2(4) - 1
x = 8 - 1
x = 7
Therefore, the cost of one scarf is $7, and the cost of one hat is $4.