Martin and Eva pool their loose change to buy snacks on their coffee break. One day they spent 6.75 on 1 carton of milk 2 donuts and 1 cup of coffee The next day they spent 8.50 on 3 donuts and 2 cups of coffee. The third day they bought 1 carton of milk 1 donut and 2 cups of coffee and spent 7.25. On the fourth day, they have a total of 6.45 left.
Is it enough to buy 2 cartons of milk and 2 donuts?

step-by-step explanation: i dont

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb