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Question

The weekly salaries of musicains in orchestras ranged from $734-$1925. Orchestras have different season lengths ranging from 24-52 weeks. In one season, what is the positive difference between the most and least that could be earned in a year?

I want to make a bracelet with seven beads. Of the seven, one bead is unique and the other six are three distnct pairs of matching beads. If the bracelts beadpattern is symmetric when the bracelt is not clasped, how many distnictbracelets can she make?

A staircase is built by stacking rectangular railroad ties that measure 1 foot by 1 foot be 3 feet. Continuing the pattern how many ties must be used to make a staircase 10 feet high?

Each of four test scores in Connies class is to be weighted equally. On the first three tests Connis scored 79%, 87%, and 98%. What percent must she score on her fourth test to have an overall average of exactly 90%?

What is a mean of numbers?

Answer 1

question 1)
the most someone could make in the orchestra in a year would be 1925/week for 52 weeks (the most money per week multiplied by the longest season length) which is $100,100. The least is 734 * 24 = $17,616. Subtracting this from the larger, we find the difference between the two to be $82,484.

Question 2)
Since the bracelet is symmetrical, the unique bead must be in the center of it, leaving room for three beads on either side. The placement of one half of the beads will determine the other half (once again, due to it's symmetry) so we would have 3 choices of color for the first bead, 2 for the second and one for the third, which would dictate the other half of the bracelet...so, 3*2*1 tells us there are 6 distinct possibilities.

Question 3)
1 tie for the first step, 2 for the second, 3 the third, etc will mean that we will need 1+2+3+4+5+6+7+8+9+10 ties all together, or 55 ties.

Question 4)
An easy averaging question. The set up is (79+87+98+x)/4 = 90. That is, the 3 tests we know the grade on added to the fourth unknown (x) test, divided by 4 (to average tham) has to be equal to 90. Solve for x by first multiplying both sides by 4 to get rid of the fraction.

79+87+98+x=360

then combine like terms:

264+x=360

subtract 264 from each side:
x=96
Connie needs a 96 on her last test.

Answer 2

1. The least that could be earned is 24 weeks x $734 or $17,616. The most is 52 weeks x $1,925 or $100,100.
$100,100 - 17,616 = $82,484

2. I think there is an applicable formula, but it has been over 40 years since I took a math class, so I don't remember it. However, if you diagram the possible combinations of beads, there are at least six combinations. If you assign numbers 1, 2, and 3 to the three pairs, then they could be arranged 123, 132, 213, 231, 321, and 312.

3. This one probably requires more thought than I can muster at this hour, but think of it this way--the first step takes one tie, the second one two (because you have to stack them to get the next step up), the third 3 and so on, so 1+2+3+4+5+6+7+8+9+10 = 55 ties.

4. To get 90%, the three scores must total 360 because 360/4 = 90. Since 79+87+98 = 264 and 360-264 = 96, then you need to score a 96% to get an average of 90%.