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Originally Posted by

**amy07** Solve For b: ax(squared) + bx+c=y.

this means that we want to get b on one side of the equation by itself. so get rid of everything on the same side with b.

$\displaystyle ax^2 + bx + c = y$ .......subtract $\displaystyle ax^2 + c$ from both sides

$\displaystyle \Rightarrow bx = y - ax^2 - c$ .........now if $\displaystyle x \ne 0$ we can divide by it.

$\displaystyle \Rightarrow b = \frac yx - ax - \frac cx$

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Three times the larger of 2 consecutive even intergers, decreased by the smaller is 58. Find the numbers.

Let $\displaystyle n$ be the smallest even integer.

Then $\displaystyle n + 2$ is the next even integer.

we are told that 3 times $\displaystyle (n + 2)$, subtracting the smaller is 58. thus,

$\displaystyle 3(n + 2) - n = 58$

now solve for $\displaystyle n$ so you can find the integers.

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Find 3 consecutive intergers such that the sum of the first two is 74 more than the third.

Let the first integer be $\displaystyle n$

then the next is $\displaystyle n + 1$

and the largest is $\displaystyle n + 2$

the sum of the first two is 74 + the third. thus,

$\displaystyle n + (n + 1) = 74 + (n + 2)$

now solve for $\displaystyle n$ to find the integers

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A pipe is 48 inches long. David wants to cut the pipe into three pieces so that the second piece is 1 inch less than the length of the third. The first piece is 5 times as long as the third. How long is each piece?

Let $\displaystyle a$ be the length of the first piece,

Let $\displaystyle b$ be the length of the second piece,

Let $\displaystyle c$ be the length of the third piece,

then we have $\displaystyle a + b + c = 48$ .................(1)

since the second piece is 1 inch less than the length of the third, we have:

$\displaystyle b = c - 1$

$\displaystyle \Rightarrow b - c = -1$ .....................(2)

since the first piece is 5 times as long as the third, we have:

$\displaystyle a = 5c$

$\displaystyle a - 5c = 0$ ........................(3)

thus we obtain the system:

$\displaystyle a + b + c = 48$ ......................(1)

$\displaystyle b - c = -1$ ............................(2)

$\displaystyle a - 5c = 0$ .............................(3)

now solve this system to get $\displaystyle a,b, \mbox{ and } c$

if you do not know how to solve simultaneous equations, you can do this in one variable.

Let the length of the third be $\displaystyle a$

then the length of the second is $\displaystyle a - 1$

and the length of the first is $\displaystyle 5a$

the pieces add up to 48, so:

$\displaystyle a + (a - 1) + 5a = 48$

now just find $\displaystyle a$, and then substitute its values into the equation to find the other pieces

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Ron runs a ski train. One day he noticed that the train contained 13 more women than men *including himself*. If there were a total of 165 people on the train, how many of them were men?

Let's keep this in one variable:

Let the number of men be $\displaystyle m$.

since the train contained 13 more women than men, the number of women is $\displaystyle m + 13$.

these must add up to 165 people, thus:

$\displaystyle m + (m + 13) = 165$

now solve for $\displaystyle m$