3. at a bargain store, tanya bought 3 items that each cost the same amount. tony bought 4 items that each cost the same amount, but each was $2.25 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.

3x = 4(x-2.25)

3x = 4x-9

add 9 to both sides

3x+9 =4x

subtract 3 x from each side

x=9

Tonya's items were $9 each

Tony's items were 9-2.25 = 6.75 each

check:

9*3=27

4 *6.75 = 27

(–1, 1) and (–6, –1)

(1, 0) and (6, 2)

(3, 0) and (8, 2)

Step-by-step explanation:

Slope of line having points (x1, y1) and (x2,y2) is given by (y2-y1)/(x2-x1)

Two lines with slope m1 and m2 are parallel if there slopes are equal i.e m1 = m2.

Slope of line  that contains (3, 4) and (–2, 2)

m = (2-4)/(-2-3) = -2/-5 = 2/5

To find if other pair of lines lie on line parallel to  line  that contains (3, 4) and (–2, 2), we need to find slope for other pair of points , if those pairs have slopes as 2/5 then its clear that they lie on line parallel to  line  that contains (3, 4) and (–2, 2) else not.

Lets find slope of all the pairs

(–2, –5) and (–7, –3)

m1 = -3 -(-5)/-7-(-2) = -3+5/-7+2

m1 = 2/-5 = -2/5

as  -2/5 is not equal to 2/5, the mentioned points do not  lie on line parallel to  line  that contains (3, 4) and (–2, 2).

(–1, 1) and (–6, –1)

m2 = -1 -1)/-6-(-1) = -2/-6+1

m2 = -2/-5 = 2/5

as  2/5 is  equal to 2/5, the mentioned points do  lie on line parallel to  line  that contains (3, 4) and (–2, 2).

(0, 0) and (2, 5)

m3 = 5 -0)/2-0

m3 = 5/2

as   5/2 is not equal to 2/5, the mentioned points do not lie on line parallel to  line  that contains (3, 4) and (–2, 2).

(1, 0) and (6, 2)

m4 = 2 -0)/6-1

m4 = 2/5

as  m4

As m4 is  equal to 2/5, the mentioned points do  lie on line parallel to  line  that contains (3, 4) and (–2, 2).

(3, 0) and (8, 2)

m5 = 2 -0)/8-3

m5 = 2/5

as  m5 is  equal to 2/5, the mentioned points do  lie on line parallel to  line  that contains (3, 4) and (–2, 2).

Thus, pair of points which lie on  lie on line parallel to  line  that contains (3, 4) and (–2, 2) are

(–1, 1) and (–6, –1)

(1, 0) and (6, 2)

(3, 0) and (8, 2)