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anonymous

  • 5 years ago

Joe has a collection of nickels and dimes that is worth $2.10. If the number of dimes was tripled and the number of nickels was increased by 24, the value of the coins would be $5.70. How many nickels and dimes does he have?

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  1. anonymous
    • 5 years ago
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    This is a two variable two equation type problem. The first one is .05x + .10y = 2.10 where x is the number of nickels and y is the number of dimes. Ex. if you had 7 nickels and 8 dimes you would take .05 times 7 to find the value of the nickels (.35) and .10 * 8 to get the value of the dimes (.80) and then add them together to get the value of the coins. 2nd equation would be .05(x + 24) + .10(3y) = 5.70 so .05x + .10y = 2.10 -- multiply every term by 100 to get rid of decimals 5x + 10Y = 210 2nd equation .05(x + 24) + .10(3y) = 5.70 distribute .05x + 1.20 + .30y = 5.70 I would multiply all terms by 100 to get 5x + 120 + 30y = 570 subtract 120 from each side 5x + 30y = 450 So you have 5x + 10y = 210 5x + 30Y = 450 subtract the bottom which means to change the signs on every term on the bottom 5x + 10Y = 210 -5x -30Y = -450 Add.. x's are gone leaving you -20Y = -240 divide by -20 Y = 12 Substitue Y = 12 into any equation and solve for X 5x + 10Y = 210 5X + 10(12) = 210 5X + 120 = 210 5X = 90 X = 18 So 18 nickels and 12 dimes

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