A 36 foot long tube is cut into two pieces with ratio 4:5. Find the length of the shorter piece.

Let 'x' and 'y' are the lengths of the two pieces then:

x + y = 36

x : y = 4 : 5 cross multiply

5x = 4y

by solving the system of equations

x + y = 36

5x = 4y

we find

x = 16 ft

y = 20 ft

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the length of the shorter piece is 16 ft.

A large square pizza has 49 pieces(square slices) John,Jack,and Jane ate all the pieces in the ratio 4:2:1 RESPECTIVELY. HOW MANY PIECES DID JACK EAT?

let x, y, and z are the number of pieces that John, Jack, and Jane ate respectively then

x + y + z = 49

x : y : z = 4 : 2 : 1

means

x = 2y = 4z

by solving the system of equations

x + y + z = 49

x = 2y

2y = 4z

we find

x = 28 pieces

y = 14 pieces

z = 7 pieces

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Jack ate 14 pieces of pizza.

The sum of two numbers is 31. Twice the smaller number is 11 more than the larger number. The positive difference between the number is?

Let 'x' and 'y' be the two numbers and x>y

x + y = 31

Twice the smaller number is 11 more than the larger number

2y = 11 + x

by solving the system of equations

x + y = 31

2y = 11 + x

we find

x = 17

y = 14

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17 - 14 = 3

the positive difference between the numbers is 3.