Chapman’s brickyard sells bricks and blocks. a brick costs $0.38 and a block costs $1.56. the brickyard filled a $24.80 order, which contained 28 items a. write a system of equations that can be used to find the number of bricks and blocks in the order. b. how many blocks were in the order?

(a) A system of equations:

(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.

⇒                          ......[1]

Since, it contained 28 items.

⇒                                               ....[2]

Multiply equation [2] both sides by 0.38 we have;

Using distributive property:

0.38x +0.38 y = 10.64                                        ......[3]

Subtract equation [3] from [1] to get x eliminated ;

Combine like terms;

1.18y =14.16

Divide both sides by 1.18 we have;

Simplify:

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:

(b)

The number of blocks are in order(y), is  12.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.