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# Algebra/Math

Question
QUESTION: I have two questions.
The directions on the bottle say two teaspoons. There are 3 teaspoons in a tablespoon and two tablespoons in an ounce. A bottle has 14 ounces and is bought in a pack of 4 bottles. How many doses are there in the pack of bottles?

The earth travels about 940,000,000 in a year. How fast is that in miles per hour using the conversion 1 mile=1.6 km?

ANSWER: 4 bottles contain 14*4 =56 ounces

56 ounces is equivalent to 56*2 =112 tablespoons

112 tablespoons is equivalent to 112*3 = 336 teaspoons

Since a dose is defined as 2 teaspoons, in the pack of 4 bottles, there are 336/2 = 168 doses (shown)

For the second problem, I am assuming you are saying the earth travels 940,000,000 km   in a year?

If so,

The earth will travel 940,000,000/365 = 2,575,000 km in a day.

Recognize that 257, 500, 000 km is equivalent to 2,575,000 / 1.6 = 1, 609, 000 miles

ie we can also say that it travels 1, 609, 000 miles in a day.

Since a day has 24 hours, it will travel 1, 609, 000 /24 =  67,050 miles in an hour.

In other words, its speed is simply 67,050 miles per hour (shown)

Hope these help. peace.

---------- FOLLOW-UP ----------

QUESTION: Phoebe Small has 35 pages of history to be read after she has been reading for ten minutes and 5 pages left after she has been reading for 50 minutes. Assume that the number of pages left to read varies linearly with the number of minutes she has been reading.
A) Write and the linear model that represents how many pages left to read and minutes read.
B) How many pages does she have to read in all?
C) When does she finish?

(A) Let the number of pages she has left to read after t minutes be y.

An appropriate model would therefore be y = kt+c, where k and c are real valued constants.

When t=10,  y=35; when t=50,  y=5

Substituting these values into the linear model gives

35= 10k + c --------(1)    and    5 = 50k +c --------(2)

(2)-(1): -30 = 40 k ===> k = -3/4 or -0.75

Substituting this value of k back into (1) gives  35= 10(-0.75) +c ===> c = 42.5

Hence, the complete linear model is given by

y = -0.75 t + 42.5   (shown)

(B) At the very beginning, she has yet to start reading.

Hence, when t=0, y=42.5, ie she has to read 42.5 pages in all. (shown)

(C) When she finishes reading, y=0

Then t= 42.5/ 0.75 =56.67 minutes (shown)

Hope it helps. Peace.
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Algebra

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#### Frederick Koh

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I can answer questions concerning calculus, complex numbers, vectors, statistics , algebra and trigonometry for the O level, A level and 1st/2nd year college math/engineering student.

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