Respuesta :
Answer:
(a) A system of equations:
[tex]0.38x+1.56y = 24.80[/tex]
[tex]x+y = 28[/tex]
(b) Number of blocks were in the order is, 12
Step-by-step explanation:
(a)
Let x represents the number of bricks and y represents the number of blocks.
As per the given statement:
A bricks costs $ 0.38 and a block costs $1.56.
Total bricks costs = 0.38x and total block costs = 1.56y
The brickyard filled $24.80 order.
⇒ [tex]0.38x+1.56y = 24.80[/tex] ......[1]
Since, it contained 28 items.
⇒[tex]x+y = 28[/tex] ....[2]
Multiply equation [2] both sides by 0.38 we have;
[tex]0.38(x+y) = 0.38 \times 28[/tex]
Using distributive property: [tex]a\cdot (b+c) = a\cdot b + a\cdot c[/tex]
0.38x +0.38 y = 10.64 ......[3]
Subtract equation [3] from [1] to get x eliminated ;
[tex]0.38x+1.56y -0.38x -0.38y= 24.80 - 10.64[/tex]
Combine like terms;
1.18y =14.16
Divide both sides by 1.18 we have;
[tex]\frac{1.18y}{1.18} = \frac{14.16}{1.18}[/tex]
Simplify:
[tex]y = 12[/tex]
Substitutes this y value in equation [2] to solve for x;
x + 12= 28
Subtract 12 from both sides we get;
x +12-12 =28-12
Simplify:
x = 16
Therefore, a system of equations that can be used to find the number of bricks and the number of blocks in the order:
[tex]0.38x+1.56y = 24.80[/tex]
[tex]x+y = 28[/tex]
(b)
The number of blocks are in order(y), is 12.
