What's the fastest way to do these math problems?

jamesford
Tue, 21 Jul 2009 18:11:15 +0000

R is the midpoint of line segment PT, and Q is the midpoint of line segment PR. If S is a point between R and T such that QS = 10 and PS = 19, what is the length of segment ST?

Doing it timed I did it in a fairly complicated way, but reviewing my work I did it an easier way.

PQ = PS - QS
= 19 - 10
= 9

Hence QR is also 9.

QS = 10, and QR + RS = QS = 10 so RS = 1.

PR = 18 = RT = RS + ST
18 = 1 + ST
ST = 17

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A phone company charges x cents for the first minute of a call and charges for any additional time at the rate of y cents per minute. If a call costs $5.55 and lasts more than 1 minute, what is the expression that represents the length of the call in minutes?

I let x = 5 and y = 10. So the number of additional minutes is (555 - 5)/10 = 55. Adding on the first minute, we get 56.

The expression then is (555 - x)/y + 1 which is the same as (555 - x + y)/y