At a bargain store, tanya bought 3 items that each cost the same amount. tony bought 5 items that each cost the same amount, but each was $1.50 less than the items that tanya bought. both tanya and tony paid the same amount of money. what was the individual cost of each person's items? (a) write an equation. let x represent the cost of one of tanya's items. (b) solve the equation. show your work. (c) check your solution. show your work. (d) state the solution in complete sentences.

Part a)

Part b)

Part c) see the explanation in Part c)

Part d) see the explanation in Part d)

Step-by-step explanation:

Part a) Write an equation

Let

x -----> represent the cost of one of Tanya's items

y ----> represent the cost of one of Tony's items

we know that

Tanya bought 3 items -----> 3x

Tony bought 5 items -----> 5y----> 5(x-1.50)

If Tanya and Tony paid the same amount of money

then

The cost of three of Tanya's items is equal to the the cost of five of Tony's items

so

Part b) Solve the equation

we have

Solve for x

distribute the right side

Group terms that contain the same variable

Combine like terms'

Divide by 2 both sides

Find the value of y

Part c) Check your solution

substitute the value of x in the originally equation

----> is verified

Part d) State the solution in complete sentences

we have that

The cost of one of Tanya's items was $3.75

Tanya paid $11.25 for 3 items

The cost of one of Tony's items was $2.25

Tony paid $11.25 for 5 items

Tanya and Tony paid the same amount of money

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.