SOLUTION: Hello,can someone help me on a word problem ? Mark won 14 less than twice as many games as John. John won 2 fewer games than mark. How many games did Mark win? Thank you in advance

Question 1066544: Hello,can someone help me on a word problem ? Mark won 14 less than twice as many games as John. John won 2 fewer games than mark. How many games did Mark win? Thank you in advance !!!!!!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let m equal the number of games that mark won.
let j equal the number of games that john won.

mark won 14 less than twice as many games as john won.

m = 2j - 14

john won 2 fewer games than mark.

j = m - 2

you have two equations that need to be solved simultaneously.
this means the same solution applies to both equations.

the equations are:]
m = 2j - 14
j = m - 2

you can solve this easily by substitution.

since j = m - 2 in the second equation, replace j with m - 2 in the first equation to get:

m = 2 * (m - 2) - 14

simplify to get m = 2m - 4 - 14

simplify further to get m = 2m - 18

subtract m from both sides of the equation and add 18 to both sides of the equation to get:

18 = 2m - m

solve for m to get m = 18.

since j = m - 2, then j must be equal to 16.

go back to your original statements and see if they hold true.

first statement says that mark won 14 less than twice as many games as john.

john won 16 so twice as many is 32 minus 14 = 18.

16 is 2 less than 18.

solution looks good.

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