math 11 help (word problem)?

Question

you have been hired for a retail job and must choose between two salary structures. witch is the better plan?

plan a

a monthly salary of $325 plus 2% commition on your sales

plan b a monthly salary of $100 plus 5% commition on your sales

solve by graphing in an appropriate window.

thanks alll i needed was the equations!!

Answer 1

This is going to depend on what you think your sales are. Suppose you expect them to be some number X.

Under Plan A you get income:
Y = 325 + 0.02*X,
while under Plan B you get
Y = 100 + 0.05*X.

Graph these two lines to see for which values of expected sales (X) the income (Y) is higher under plan a vs. plan b.

Or you can do this alegbraically. Since the commission is higher under Plan B it will lead to more income if your expected sales are very large. But if your sales are very small, Plan A is better since you're guaranteed a base salary of at least $325. So there's some expected sales volume X' below which Plan A is best, and above which Plan B is best.

At X' the two plans yield identical income. Use this fact to solve
325 + 0.02*X' = 100 + 0.05*X'
for X'. The answer is X' = $7500. So for expected sales below that, go with the high base salary of Plan A. For expected sales above $7500, go with Plan B because of the high commissions.

Answer 2

The graphs are both straight lines.
$325 +2% of sales is a straight line that has a y-intercept of 325, (coordinate is (0,325)), and a slope
or 2 per 100. (m=rise/run, =2/100 or 1/50)

$100+5% has y-intercept (0,100) and slope 5/100, or
1/20.

As to which is the better plan,
The graph of Plan A has as its equation y=1/50x+325
Plan B is y=1/20x+100
The break-even point occurs when y of Plan A = y of
Plan B.
In other words, when 1/50x+325= 1/20x+100
Multiply both sides by 100 to get
2x+32500=5x+10000
-3x=-22500
3x=22500
x=7500

Below 7500 in sales, Plan A is better. At 7500, they
are equally good. Above monthly sales of $7500, Plan B is better
When you graph these two lines, they should intersect at the 7500 mark for x.

Answer 3

Two equations:
Income 1 = $325 + .02 * sales
Income 2 = $100 + .05 * sales
graph each over some range. They cross at
325 + .02 sales = 100 + .05 sales
225 = .03 sales
or
Sales = $7500
So graph over the range Sales = 5000 to 10000
Which is better? It depends upon how much you think you can sell in a month. If you can sell more than $7500, then opt for the lower fixed salary and larger commission

Answer 4

which plan is best depends on whether you make a lot of sales or a little. So,

let x= the dollar amount of your sales.
let y= your total earnings for the month

under plan a, y= 325+ .02x
under plan b, y=100+ .05x

So, graph those two lines in the same window and see at what value of x they intersect. If your sales are less than that value, plan a is better. If your sales are greater than that value, plan b is better. (Do you understand why?)

Answer 5

Oops we need a graph. Both give straight lines One with slope 2% and y intercept 325, the second with slope 5% and y intercept 100. The better option depends on the amount of sales per month you can make.