Coin Word Problems | MathHelp.com - By MathHelp.com
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| 00:00 | Martin has a total of 19 nickels and dimes worth | |
| 00:04 | a $65 . How many of each type of coin | |
| 00:08 | does he have ? Let's start this problem by setting | |
| 00:13 | up a chart down the left side . We'll have | |
| 00:24 | our different types of coins in this case . Nichols | |
| 00:32 | and dimes . Yeah . Across the top we'll have | |
| 00:38 | our formula which we talked about in the previous example | |
| 00:43 | , number of coins times the value of each coin | |
| 00:59 | equals their total value . Now let's fill out our | |
| 01:14 | chart For a number of nickels and dimes . We | |
| 01:19 | know that Martin has a total of 19 nickels and | |
| 01:22 | dimes , but we don't know how many of each | |
| 01:25 | he has . In fact , that's what the problem | |
| 01:27 | is asking . So if we represent our number of | |
| 01:31 | nickels as X , we can call our number of | |
| 01:34 | dimes 19 minus X . The value of each nickel | |
| 01:42 | is five cents . The value of each dime is | |
| 01:46 | 10 cents . Our total value based on our formula | |
| 01:53 | is going to come from the first column , times | |
| 01:56 | the second column . So the total value of our | |
| 01:59 | Nichols is X , times five or five X . | |
| 02:05 | And the total value of our dimes is 19 minus | |
| 02:08 | x . Times 10 Or 10 parentheses 19 -X . | |
| 02:16 | Our goal in this problem will be to find X | |
| 02:20 | . Because X represents our number of nickels . And | |
| 02:24 | the problem asks how many of each type of coin | |
| 02:27 | does he have ? If we know the number of | |
| 02:29 | nickels , we can easily find the number of dimes | |
| 02:33 | and we'll have our answer . But we need an | |
| 02:37 | equation in order to find X . And it's important | |
| 02:41 | to understand that the information in this equation will always | |
| 02:45 | come from the last column of your chart , the | |
| 02:49 | total value column . So what do we know about | |
| 02:53 | the total value of our nickels and the total value | |
| 02:56 | of our dimes ? Well , we know that the | |
| 02:59 | total value of all of our coins is $1.65 . | |
| 03:05 | So if we add the total value of our nickels | |
| 03:07 | plus the total value of our dimes , that should | |
| 03:10 | equal $1.65 . So down here we're going to add | |
| 03:16 | another box and inside we're gonna put 165 Notice I | |
| 03:23 | wrote a $65 in terms of sense because our value | |
| 03:28 | of nickels and value of dimes is also written in | |
| 03:31 | terms of scents and we need to be consistent . | |
| 03:35 | So here's our equation five X plus 10 Times 19 | |
| 03:46 | -X equals 165 . If we solve this , we | |
| 03:55 | get X equals five . Going back up into our | |
| 04:03 | chart , remember that X represents our number of nickels | |
| 04:08 | . So martin has five nickels To get his number | |
| 04:16 | of dimes , we take 19-1 , which is 19-5 | |
| 04:22 | or 14 dimes . And that's our answer . |
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