Question 214205: Todd has 48 words to spell for a puzzle. His mother says she will pay him $1.00 for every word he spells correctly but he has to pay her $0.60 for every word he spells incorrectly. If Todd makes $19.20, how many words did he spell correctly?
Define the variable, create the equation, and solve.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Todd has 48 words to spell for a puzzle. His mother says she will pay him $1.00 for every word he spells correctly but he has to pay her $0.60 for every word he spells incorrectly. If Todd makes $19.20, how many words did he spell correctly?
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x = number of words spelled correctly.
y = number of words spelled incorrectly.
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number of words spelled correctly plus number of words spelled incorrectly equals 48.
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x + y = 48
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x * 1.00 = amount of money he makes if he spells a word correctly.
y * .60 = amount of money he has to pay back if he spells a word incorrectly.
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number of words spelled correctly times a dollar minus the number of words spelled incorrectly times 60 cents equals 19.20
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1.00 * x - .60 * y = 19.20
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you have 2 equations that need to be solved simultaneously.
they are:
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x + y = 48
x - .6y = 19.20
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use the first equation to solve for y.
you get:
y = 48-x
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substitute for y in the second equation to get:
x - .6*(48-x) = 19.2
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remove parentheses to get:
x - .6*48 + .6x = 19.2
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simplify results and combine like terms to get:
1.6x - 28.8 = 19.2
add 28.8 to both sides of the equation to get:
1.6x = 48
divide both sides of the equation by 1.6 to get:
x = 30
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since x+y = 48, then y = 18
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plug these values into x - .6y = 19.2 to get:
30 - .6*18 = 30 - 10.8 = 19.2
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this checks out so the answer is:
number of questions answered correctly is 30 and number of questions answered incorrectly is 18.
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