Lesson Entertainment problems on proportions

Entertainment problems on proportions

Problem 1

If  6 small eggs are the same as  4 medium eggs, then

   18 small eggs are the same as 12 medium eggs.



Next,

    12 medium eggs are the same as 8 large eggs, according to the condition.



So, you have this equivalency  18 small eggs ~ 8 large eggs.



Then you can write this proportion

     = ,


or, in the shortened form

     = .



From the proportion,

    x =  =  = 11 2/8 = 11 1/4.


ANSWER.  11 1/4  small eggs  are equivalent to  5 large eggs.

Problem 2

Originally, Lorraine had                         6x pens, 13x pencils and 4x erasers.


After giving away some pencils and pens, she has 4y pens, 17y pencils and 7y erasers.


But the number of erasers didn't change;  so, 4x = 7y erasers.



Since she had 91 pencils originally, it means that 91 = 13x;  hence  x = 91/13 = 7;

so, originally Lorraine had 6*7 = 42 pencils; 13*7 = 91 pens and 4*7 = 28 erasers.



Next,  28 = 7y erasers means that  y = 28/7 = 4.

It implies, that after giving away, there are 4*4 = 16 pencils and 17*4 = 68 pens.



Thus, the number of pens    she gave away, was  91-68 = 23, 

and   the number of pencils she gave away, was  42-16 = 26.



ANSWER.  Lorraine gave away 23 pens and 26 pencils.

Problem 3

Originally, there are 70 gold coins and 50+100 = 150 not-gold coins in the treasure.


We want to add gold coins to the treasure in a way to have half of the coins in the treasure chest as a gold coins.


Obviously, the goal will be achieved, when the new total gold coins will be 150.


For it, 150-70 = 80 gold coins must be added.    ANSWER