Math Help - Story Problems

1. Story Problems

I am confused on these problems:

the measure of the complement of an angle is fifteen less than four times the measure of the angle. Find the measure of the angle and its complement.

The baseball company manufactures two grades of baseballs, the speedee, which sells for $2.10, and the Quickfire, which sells for$3.50. The company receives $843.50 for an order of 305 balls. How many of each ball were ordered? Value Hardware sells 3-in. finishing nails for 0.99/lb, and 2-in. finishing nails sell for 1.39/lb. Tony needs 5 lbs. of nails. If his bill totals$6.15, how many pounds of each size did he buy?

y varies directly as x^2

If y=4 when x=6, find y when x=9.

If y=16 when x=4, find x when y=25

2. I'll try to explain as I go along. If it clicks in your head, try to finish it yourself!

the measure of the complement of an angle is fifteen less than four times the measure of the angle. Find the measure of the angle and its complement.

Okay, the complement of the angle adds to the angle to get 90 degrees. So you know that the two angles must equal 90 degrees when added.
Let's represent the measure of the angle as a
The complement is 4a-15 because it is fifteen less (-15) than four times the angle (4a)
(4a-15) + a = 90
You can take it from there!

The baseball company manufactures two grades of baseballs, the speedee, which sells for $2.10, and the Quickfire, which sells for$3.50. The company receives $843.50 for an order of 305 balls. How many of each ball were ordered? This one is a little trickier. There is a total of 305 balls order. Somehow you need to represent the number of each type of ball ordered. Let's use a variable for the speedie balls, s. Now you know that if you subtract the number of speedie balls from the total 305 that whatever is left over has to be a Quickfire ball, so that can be represented as 305-s. The total value of these 305 balls is$843.50, so you're going to need to put the number of balls we have above in terms of actual value and add them up to get the total of $843.50. You do this by multiplying the number times the value, so for the speedie balls: (2.10)s = 2.1s and for the Quickfire: 3.50(305-s) = 1067.5 - 3.5s These two values will add up to be$843.50, so your equation will be:
2.1s + 1067.5 - 3.5s = $843.50 Once again, I'll leave it up to you to solve. Value Hardware sells 3-in. finishing nails for 0.99/lb, and 2-in. finishing nails sell for 1.39/lb. Tony needs 5 lbs. of nails. If his bill totals$6.15, how many pounds of each size did he buy?

This is similar to the last one. Let's use the variable t for the 3-in nails. The 2-in nails will be 5 - t, because after you subtract the pounds of 3-in nails he has you will have only 2-in nails left. Again we multiply these by their values, for the 3-in:
0.99(t) = 0.99t
for the 2-in:
1.39(5 - t) = 6.95 - 1.39t
These add up to the total of 6.15, so your equation is:
0.99t + 6.95 - 1.39t = 6.15

You know the drill. Good luck with your homework, and I hope I've helped you understand better!

3. Angle/Angle Compliment:

Let x = initial angle and y = x's compliment.

Based on the description, y = 4x - 15.

Because we're dealing with the compliment of an angle we have:

90 = x + 4x - 15

5x = 105

x = 21 degrees

Plugging back in to y = 4x - 15, y = 69 degrees.

Baseball Problem

This is going to be a system of equations. We know the prices of the two types of baseballs, the total price, and the amount of baseballs that were purchased. So,

2.10x + 3.50y = 843.50
x + y = 305

We solve the second equation for x and substitute in to the first equation.

2.10(305 - y) + 3.50y = 843.50

We solve this for y and get

y = 145

We plug this value in to the equation x + y = 305 and we get x = 160.
x is the baseballs that cost $2.10 and y is the baseballs that cost$3.50.

Nails Problem

Like the baseball problem above, we want to set up a system of equations. We know the price of the two types of nails, the total price, and the total lbs of nails purchased. We create the following the system:

0.99x + 1.39y = 6.15
x + y = 5

We solve the second equation for x and get

x = 5 - y, then we substitute this in to the first equation for x to get

0.99(5 - y) + 1.39y = 6.15

We solve for y and obtain that y = 3. We then plug this value in to the second equation to obtain x. We get that x = 2.

I know this doesn't answer all of your questions, but I hope this helps.

4. Originally Posted by peachgal
y varies directly as x^2

If y=4 when x=6, find y when x=9.
$y \propto x^2$

$y = k x^2$

$4 = k * 6^2$

$\frac{4}{36} = k$

$k = \frac{1}{9}$

$y = \frac{1}{9} x^2 = \frac{x^2}{9}$

Substitute x = 9 to find y.

Follow the same steps to find the value of k, given y=16 when x=4. Then solve for x when y=25.

Hope that helps.