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?

Let x represent the cost of one of Tanya's items.

Then the cost of one of Tony's items =x - 2.25. But we have:

3x =4(x - 2.25)

3x =4x - 9 subtract 3x from both sides

0 =x - 9 add 9 to both sides

x=$9 The cost of one of Tanya's items

27 Total cost of Tanya's 3 items

2.25 =$6.75 cost of one of Tony's items.

27 Total cost of Tony's 4 items.

3 x 6.75 =$27. This shows that both Tony and Tanya spent the same amount of money.

Step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

$75.00

step-by-step explanation:

i = prt

i = 1,5000 * 0.025 * 2

i = 75