document.write( "Question 101847: three footballs and one soccer ball cost $155. Two footballs and three soccer balls cost $220. Determine the cost of one football and the cost of one soccer ball. \n" ); document.write( "
Algebra.Com's Answer #74047 by doukungfoo(195)\"\" \"About 
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first set some variables
\n" ); document.write( "Let f = football cost
\n" ); document.write( "and
\n" ); document.write( "Let s = soccer ball cost
\n" ); document.write( "Now write equations from the given information
\n" ); document.write( "Given: three footballs and one soccer ball cost $155
\n" ); document.write( "ok so using the variables f and s lets write and equation
\n" ); document.write( "3f + s = 155
\n" ); document.write( "Now what else are we given?
\n" ); document.write( "Given: two footballs and three soccer balls cost $220
\n" ); document.write( "write an equation
\n" ); document.write( "2f + 3s = 220
\n" ); document.write( "Ok now we have a system of equations that we can use to solve for f and s
\n" ); document.write( "Take the first equation and set it equal to s
\n" ); document.write( "3f + s = 155
\n" ); document.write( "s = 155 - 3f
\n" ); document.write( "Now that we have s equal to 155-3f we can substitiute that into the second equation. Here goes...
\n" ); document.write( "2f + 3s = 220
\n" ); document.write( "2f + 3(155-3f) = 220
\n" ); document.write( "now we have an equation with one variable that we can solve for.
\n" ); document.write( "2f + 3(155-3f) = 220
\n" ); document.write( "distribute 3 across (155-3f)
\n" ); document.write( "or in other words multiply 3 times 155 and 3 times -3f
\n" ); document.write( "2f + 465 - 9f = 220
\n" ); document.write( "combine like terms
\n" ); document.write( "465 - 7f = 220
\n" ); document.write( "subtract 465 form both sides of the equation
\n" ); document.write( "465 - 465 - 7f = 220 - 465
\n" ); document.write( "-7f = -245
\n" ); document.write( "divide both sidse of the equation by -7
\n" ); document.write( "-7f/-7 = -245/-7
\n" ); document.write( "f = 35
\n" ); document.write( "Answer: One football costs $35.00
\n" ); document.write( "Now we can use this value for f to solve for s
\n" ); document.write( "Take the first equation and substitute f with 35
\n" ); document.write( "3f + s = 155
\n" ); document.write( "3(35) + s = 155
\n" ); document.write( "multiply 3 times 35
\n" ); document.write( "105 + s = 155
\n" ); document.write( "subtract 105 from both sides of the equation
\n" ); document.write( "105 - 105 + s = 155 -105
\n" ); document.write( "s = 50
\n" ); document.write( "Answer: One soccer ball costs $50.00
\n" ); document.write( "Check the answers by trying them in both of our orignal equations
\n" ); document.write( "3f + s = 155
\n" ); document.write( "3(35) + 50 = 155
\n" ); document.write( "105 + 50 = 155
\n" ); document.write( "155 = 155
\n" ); document.write( "That works lets try the second equation
\n" ); document.write( "2f + 3s = 220
\n" ); document.write( "2(35) + 3(50) = 220
\n" ); document.write( "70 + 150 = 220
\n" ); document.write( "220 = 220
\n" ); document.write( "That works too.
\n" ); document.write( "Conclusion:
\n" ); document.write( "We solved the system of equations by using the substitution method and checked our answers to prove them correct.\r
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