Lesson Entertainment problems on proportions
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<H2>Entertainment problems on proportions</H2> <H3>Problem 1</H3>If 6 small eggs are the same as 4 medium eggs and 6 medium eggs are the same as 4 large eggs, then how much small egg do you need for 5 large eggs ? <B>Solution</B> <pre> 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 {{{18_small_eggs/x_small_eggs}}} = {{{8_large_eggs/5_large_eggs}}}, or, in the shortened form {{{18/x}}} = {{{8/5}}}. From the proportion, x = {{{(18*5)/8}}} = {{{90/8}}} = 11 2/8 = 11 1/4. <U>ANSWER</U>. 11 1/4 small eggs are equivalent to 5 large eggs. </pre> <H3>Problem 2</H3>Lorraine bought some stationery. The ratio of pens to to pencils to erasers is 6 to 13 to 4. She then gave away some pencils and pens. The ratio of pens to pencils to erasers left was 4 to 17 to 7. If she had 91 pencils at first how many pens and pencils did she give away ? <B>Solution</B> <pre> 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. <U>ANSWER</U>. Lorraine gave away 23 pens and 26 pencils. </pre> <H3>Problem 3</H3>A treasure chest contains 70 gold coins, 50 silver coins, and 100 bronze coins. How many additional gold coins must be added to the 220 coins already in the treasure chest so that half of the coins in the treasure chest are gold? <B>Solution</B> <pre> 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. <U>ANSWER</U> </pre> My other lessons on <B>proportions</B> in this site are - <A HREF=http://www.algebra.com/algebra/homework/proportions/lessons/-Proprtions.lesson>Proportions</A> - <A HREF=http://www.algebra.com/algebra/homework/proportions/lessons/Using-proportions-to-solve-word-problems.lesson>Using proportions to solve word problems</A> - <A HREF=http://www.algebra.com/algebra/homework/proportions/lessons/Using-proportions-to-solve-word-problems-in-Physics.lesson>Using proportions to solve word problems in Physics</A> - <A HREF=http://www.algebra.com/algebra/homework/proportions/lessons/Using-proportions-to-solve-Chemistry-problems.lesson>Using proportions to solve Chemistry problems</A> - <A HREF=https://www.algebra.com/algebra/homework/proportions/lessons/Typical-problems-on-proportions.lesson>Typical problems on proportions</A> - <A HREF=http://www.algebra.com/algebra/homework/proportions/lessons/Using-proportions-to-estimate-the-number-of-fish-in-a-lake.lesson>Using proportions to estimate the number of fish in a lake</A> - <A HREF=http://www.algebra.com/algebra/homework/proportions/lessons/HOW-TO-algebreze-and-solve-this-problem-using-proportions.lesson>HOW TO algebraize and solve these problems using proportions</A> - <A HREF=https://www.algebra.com/algebra/homework/proportions/lessons/Using-proportions-to-solve-word-problems-in-Geometry.lesson>Using proportions to solve word problems in Geometry</A> - <A HREF=https://www.algebra.com/algebra/homework/proportions/lessons/Using-proportions-to-solve-some-nice-simple-Travel-and-Distance-problems.lesson>Using proportions to solve some nice simple Travel and Distance problems</A> - <A HREF=https://www.algebra.com/algebra/homework/proportions/lessons/Miscellaneous-problems-on--proportions.lesson>Advanced problems on proportions</A> - <A HREF=https://www.algebra.com/algebra/homework/proportions/lessons/Problems-on-proportions-for-mental-solution.lesson>Problems on proportions for mental solution</A> - <A HREF=https://www.algebra.com/algebra/homework/proportions/Selected-problems-on-proportions-from-the-archive.lesson>Selected problems on proportions from the archive</A> - <A HREF=http://www.algebra.com/algebra/homework/proportions/lessons/OVERVIEW-of-lessons-on-proportions.lesson>OVERVIEW of lessons on proportions</A>
