Percents

Question

Yesterday, Teddy played a game repeatedly on his computer and won exactly 85% of the games he played. Today, Teddy played the same game repeatedly, winning every game he played, until his over-all winning percentage for yesterday and today was exactly 94%. What is the minimum number of games that he played today?

Answer 1

Unless we know how many games were played yesterday, we can only give a percentage, rather than a specific number.

 

First identify the quantities involved

Let m = number of games played yesterday

Let n = number of games played today

 

Next Translate the words into equation relating the quantities.

The percentage won =

(games won)/(games played)

 

(.85 * m + n) / (m + n) = .94

 

Snce we only have one equation for two unknowns, all we can do is arrive at a relationship.

 

So, multiply both sides by the denominator

.85*m +n = .94*(m+n)

multiply them out

.85m + n = .94m + .94 n

now collect ms on one side and ns on the other

.06n = .09m

finally, divide by .06 and by m

n/m = .09/06

simplify

n/m = 3/2

 

So the answer to “how many games did Teddy play today?” Is “3/2 as many as he played yesterday”.