Question 885086: Andy has 14 coins made up of quarters and half dollars their total value is$6.00 how many quarters does he have Found 2 solutions by jim_thompson5910, algebrapro18:Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website! Hint: He has 14 coins (quarters and half dollars only), so . The variable q is the number of quarters and h is the number of half dollars.
You can put this solution on YOUR website! Well lets let q be the number of quarters Andy has and lets let h be the number of half dollars Andy has. We know that he has 14 coins so writing that as an equation we get:
We also know that he has 6 dollars worth of coins and that quarters are worth 25 cents and half dollars are worth 50 cents. So we multiply the 25 cents times the number of quarters he has and add that to 50 cents times the number of half dollars he has and that's going to equal the total of 6 dollars. Writing that as an equation we get(note that cents are written as decimals):
You can work this problem with the decimals in there if you want but I for one don't like decimals and since these both have the same number of digits past the decimal point we can multiply the whole equation by 100 to clear the decimals.
100*
So now we have our two equations as:
Now we can solve equation 1 for either q or h it doesn't matter. I'll solve for q.
subtract h from both sides to get q by its self
Now we can plug our equation for q into the second equation and solve for h.
plug in 14-h for q distribute the 25 combine like terms subtract 350 from each side divide both sides by 25
So we know that he has 10 half dollars but we still need to figure out how many quarters he has. We saw earlier that he has 14 minus the number of half dollars he has in quarters. So he has 14-10 = 4 quarters.
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