Tad and Timothy went to the paint store together. Tad bought 6 cans of paint
and 1 paint brush for $67. Timothy bought 4 cans of the same paint and 3 of
the same type of paint brushes. Timothy’s total cost was $54.
Write a linear equation that represents Tad’s purchase and another
to represent Timothy’s purchase. Let x represent the cost of a can of
paint and y represent the cost of a paint brush.
b. Solve the system of linear equations using the substitution method.
c. What was the cost for a can of paint? The cost of a paint brush?
i dont get ur answer
a. Let's represent Tad's purchase:
Cost of 6 cans of paint + Cost of 1 paint brush = $67
6x + y = 67
Similarly, Timothy's purchase can be represented as:
Cost of 4 cans of paint + Cost of 3 paint brushes = $54
4x + 3y = 54
b. To solve the system of linear equations using the substitution method, we can solve one equation for one variable and substitute it into the other equation.
From equation 1:
6x + y = 67
y = 67 - 6x
Substitute y = 67 - 6x into equation 2:
4x + 3(67 - 6x) = 54
4x + 201 - 18x = 54
-14x + 201 = 54
-14x = 54 - 201
-14x = -147
x = -147 / -14
x = 10.5
Now, substitute the value of x into equation 1 to find y:
y = 67 - 6(10.5)
y = 67 - 63
y = 4
c. The cost for a can of paint is $10.50 and the cost of a paint brush is $4.
a) Let's set up the linear equations to represent Tad's and Timothy's purchases:
For Tad:
Equation 1: 6x + y = 67
(The cost of 6 cans of paint plus the cost of 1 paint brush equals $67)
For Timothy:
Equation 2: 4x + 3y = 54
(The cost of 4 cans of paint plus the cost of 3 paint brushes equals $54)
b) Now, let's solve the system of linear equations using the substitution method:
First, solve Equation 1 for y:
y = 67 - 6x
Now substitute this value of y into Equation 2:
4x + 3(67 - 6x) = 54
4x + 201 - 18x = 54
-14x = -147
x = 10.5
Now substitute x = 10.5 into Equation 1:
6(10.5) + y = 67
63 + y = 67
y = 4
So the cost for a can of paint is $10.5 and the cost of a paint brush is $4.
c) The cost for a can of paint is $10.5 and the cost of a paint brush is $4.
I am going to use c and b so I do not get confused (I confuse easily)
67 = 6 c + 1 b
54 = 4 c + 3 b
so 1 b = 67 - 6 c
substitute that in the second equation
54 = 4 c + 3 (67 - 6 c)
54 = 4 c + 201 - 18 c
14 c = 147
c = $10.50
b = 67 - 6*10.5 = $4.00