I have four rectangular pieces of thin hardboard whose dimensions (in cm) are 55×85, 65×75, 65×85 and 90×105.

Without bending the hardboard, how many of these can I get through an open rectangular window measuring 60cm×80cm?

All of them

Step-by-step explanation:

Longest edge that can pass through this window is:

sqrt(60² + 80²)

sqrt(10000)

100

(The diagonal)

Since all of the pieces have atleast one length less than 100, all can pass through the window

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.