Answer:
(a) The equality that express many bottles of paint, x, and boxes of colored pencils, y, Carmen can buy is 2 x + 3.5 y = 42
b)Three different solutions:
x = 14, y = 4 is First Solution.
x = 7, y = 8 is Second Solution.
x = 21, y = 0 is Third Solution.
Step-by-step explanation:
Here, the cost of 1 bottle of paint = $2.00 each
The cost of 1 box of colored pencils = $3.5 each
Let us assume the number of bottle of paints purchased = x
So, the cost of x bottle of paints = x ( Cost of 1 bottle of paint)
= x ($2.00) = 2 x
Also, assume the number of box of colored pencils purchased = y
So, the cost of y box of colored pencils = y ( Cost of 1 box)
= y ($3.50) = 3.5 y
Also, the total amount to be spent on art supplies = $42
So, the total amount spent on x paint bottles + y box of colored pencil
= $42
or, 2 x + 3.5 y = 42
a ) So, the equality that express many bottles of paint, x, and boxes of colored pencils, y, Carmen can buy is 2 x + 3.5 y = 42
b)Three different solutions:
When y = 4 , equation is: 2 x + 3.5(4) = 42
or, 2 x = 42 - 14 = 28, or x = 28/2 = 14
So, x = 14, y = 4 is First Solution.
When y = 8 , equation is: 2 x + 3.5(8) = 42
or, 2 x = 42 - 28 = 14, or x = 14/2 = 7
So, x = 7, y = 8 is Second Solution.
When y = 0 , equation is: 2 x + 3.5(0) = 42
or, 2 x = 42 , or x = 42/2 = 21
So, x = 21, y = 0 is Third Solution.
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