SAT math questions?

Question

1. If a over x minus b over y = c and xy = 1 over c, then bx = ?

2. Pipe 1 can fill a tank in 3 hours. Pipe 2 can fill the same tank in 5 hours. To the nearest hour, how long would it take both pipes working together to fill the tank?

3. Which of the following can be used to find a woman's present age if she is now 6 times as old as her son and next year her age will be equal to the square of her son's age?

A. 6w + 1 = w^2 + 1
B. 6(w + 1) = w^2 + 1
C. 6(w + 1) = (w + 1)^2
D. 6w + 1 = (w + 1)^2
E. w + 6 = (w + 1)^2

Thank you! Please show steps/reasoning if possible thanks again for any help :].

Answer 1

Hi,

1. Given the equations:

1
---.=.xy
c


a......b
---.-..---.=.c
x.......y

Multiply each term by xy to eliminate the fractions in the second equation.

axy....bxy
-----.-..---.=.cxy
x.........y

Simplifying this gives the equation:

ay - bx = cxy

Since xy = 1/c, replace xy with the fraction 1/c.

ay - bx = c(1/c)

ay - bx = 1

To solve this for bx, add bx and subtract 1.

ay - bx = 1

ay = bx + 1

ay - 1 = bx <== answer
This is the same as bx = ay - 1.

2. A work equation is:

time.................time
together..........together
-------------...+..------------- = 1
time A..............time B
alone................alone

This problem would be:

x......x
--.+.-- = 1
3.....5

To solve multiply by the LCD, 15.

15x...15x
-----.+.---- = 15
..3.......5

5x + 3x = 15
8x = 15
x = 15/8 or 1.875 hours
To the nearest hour that would be about 2 hours.


3. If the son's present age is "w", then mom's present age is "6w". In one year she will be 6w + 1 and her son will be
w + 1. At that time, her age, 6w + 1, equals her son's age, w + 1, squared. The equation is answer D.

mom's age in 1 year equals son's age in 1 year, squared

...........6w + 1...............=.....(x.+.1)²

For what it is worth, the son is 4 now and mom is now 24. In a year the mom will be 25 and her age will be the square of her son's age then, 5.


I hope that helps!! :-)

Answer 2

3.

she is now 6 times as old as her son:

w = 6 * s

next year her age will be equal to the square of her son's age:

w + 1 = (s + 1)^2