Astore sold 21 sweatshirts. white ones cost $10.95 and yellow ones cost $12.50. in all, $260.95 worth of sweatshirts were sold. how many of each color were sold?

The store sold 1 white sweatshirt and 20 yellow sweatshirts

Step-by-step explanation:

Step 1: Express total cost of sweatshirts

Total cost of sweatshirts can be expressed as;

Total cost=(price per white sweatshirt×number of white sweatshirts sold)+(price per yellow sweatshirt×number of yellow sweatshirt sold )

where;

Total cost=$260.95

Price per white sweatshirt=$10.95

number of white sweatshirts sold=w

Price per yellow sweatshirt=$12.50

number of yellow sweatshirt sold=y

Replacing;

260.95=(10.95×w)+(12.5×y)

10.95 w+12.5 y=260.95...equation 1

Step 2: Express total number of sweat shirts sold

Total number of sweatshirts sold=number of white sweatshirts sold+number of yellow sweatshirt sold

where;

Total number of sweatshirts sold=21

number of white sweatshirts sold=w

number of yellow sweatshirt sold=y

replacing;

w+y=21...equation 2

Step 3: Solve simultaneously equation 1 and 2

1(10.95 w+12.5 y=260.95)>>>10.95 w+12.5 y=260.95

-

12.5(w+y=21)>>>12.5 w+12.5 y=262.5

(10.95 w-12.5 w)+(12.5 y-12.5 y)=260.95-262.50

-1.55 w=-1.55

w=1.55/1.55

w=1

Replace the value of w in equation 2

w+y=21

1+y=21

y=21-1=20

The store sold 1 white sweatshirt and 20 yellow sweatshirts

A)  both functions are linear

B) f(x) = 7446.4x + 178713.6 and f(x) = 11000x + 179000

C) House 2 will value $106894.4 more than house 1.

Step-by-step explanation:

A) Value Increase from year 1 to year 2:

House 1: 193,606.40 - 186,160 = 7446.4

House 2: 201,000 - 190,000 = 11000

Value Increase from year 2 to year 3:

House 1: 201,350.66 - 193,606.40 = 7744.26

House 2: 212,000 - 201,000 = 11000  

This means that a constant increament in x variable gives a constant increament in both houses vales. Then, both functions are linear.

B) The slope is the same as the value increment from one year to the next one.

slope (m) of House 1: 7446.4

slope (m) of House 2: 11000

General formula of a line:

f(x) = mx+b

Replacing with a known point:

House 1

186,160 = 7446.4(1) + b

b = 186,160 - 7446.4 = 178713.6

equation: f(x) = 7446.4x + 178713.6

House 2

190,000 = 11000(1) + b

b = 190,000 - 11000 = 179000

equation: f(x) = 11000x + 179000

C) Replacing x = 30 into each equaiton:

Value of House 1 after 30 years

f(x) = 7446.4(30) + 178713.6 = 402105.6

Value of House 2 after 30 years

f(30) = 11000(30) + 179000 = 509000

Then, house 2 will value 509000 - 402105.6 = $106894.4  more than house 1.