Lesson How many coconuts are there in each of five baskets?
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<H2>How many coconuts are there in each of five baskets?</H2> <H3>Problem 1</H3>Five baskets contain coconuts. The first and second baskets together have a total of 52 coconuts. The second and third baskets have 43 coconuts. The third and fourth baskets have 34 coconuts. The fourth and fifth baskets have 30 coconuts, and the first and fifth baskets have 47 coconuts. How many coconuts are in each basket? <B>Solution</B> <pre> Let {{{x[i]}}} be the number of coconuts in the i-th basket, i = 1, 2, 3, 4, 5. Then we have this system of 5 equations in 5 unknowns: {{{x[1]}}} + {{{x[2]}}} = 52, (1) {{{x[2]}}} + {{{x[3]}}} = 43, (2) {{{x[3]}}} + {{{x[4]}}} = 34, (3) {{{x[4]}}} + {{{x[5]}}} = 30, (4) {{{x[1]}}} + {{{x[5]}}} = 47. (5) Add all 5 equations (1) to (5) (both sides). You will get {{{2*(x[1] + x[2] + x[3] + x[4] + x[5])}}} = 206, or, dividing both sides by 2 {{{x[1] + x[2] + x[3] + x[4] + x[5]}}} = 103. (6). Now, add equations (1) and (4) and distract this sum from (6). You will get {{{x[3]}}} = 103 - 52 - 30 = 21. So, there are 21 coconuts in basket #3. Next, from equation (2) you can easily get get {{{x[2]}}} = 43 - {{{x[3]}}} = 43 - 21 = 22. So, there are 22 coconuts in basket #2. Then from equation (1) you can easily get {{{x[1]}}} = 52 - {{{x[2]}}} = 52 - 22 = 30. So, there are 30 coconuts in basket #1. Similarly, from equation (3) you can easily get {{{x[4]}}} = 34 - {{{x[3]}}} = 34 - 21 = 13. So, there are 13 coconuts in basket #4. Then from (4) you have {{{x[5]}}} = 30 - {{{x[4]}}} = 30 - 13 = 17 coconuts in basket #5. <U>Answer</U>. 30, 22, 21, 13 and 17 coconuts in baskets 1 to 5 respectively. </pre> My other lessons on Miscellaneous word problems in this site are <TABLE> <TR> <TD> - <A HREF=http://www.algebra.com/algebra/homework/word/misc/Some-Logic-problems.lesson>Some logic problems</A> - <A HREF=http://www.algebra.com/algebra/homework/word/misc/HOW-TO-algebreze-and-to-solve-word-problems-on-numbers.lesson>How to algebreze and to solve word problems on numbers?</A> - <A HREF=http://www.algebra.com/algebra/homework/word/misc/Problem-on-two-wheels-and-three-wheels-bicycles-in-a-sale.lesson>Problem on two-wheel and three-wheel bicycles</A> - <A HREF=http://www.algebra.com/algebra/homework/word/misc/Problem-on-animals-at-a-farm.lesson>Problem on animals at a farm</A> - <A HREF=http://www.algebra.com/algebra/homework/word/misc/Problem-on-tablets-in-containers.lesson>Problem on pills in containers</A> - <A HREF=http://www.algebra.com/algebra/homework/word/misc/What-type-of-problems-are-these.lesson>What type of problems are these?</A> - 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