The sum of two numbers is 30 and their difference is 6
1 answer:
I'm going to assume that you are trying to find the two numbers. Based on the information in the problem, we can create the following equations (where and
are the two numbers):
We have a systems of equations. In this case, it would be easier to use elimination by adding vertically. This produces the result:
To find , substitute the value for
into one of the earlier equations:
The two numbers are 12 and 18.
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Question:
A salesperson earns commission on the sales that she makes each month.
The salesperson earns a 5% commission on the first $5,000 she has in sales.
The salesperson earns a 7.5% commission on the amount on her sales that are greater than $5,000.
Part A:
This month the salesperson had $8,000 in sales. What amount of commission, in dollars, did she earn?
Part B:
The salesperson earned $1,375 in commission, last month. How much money, in dollars, did she have in sales last month?
Answer:
A) The amount of commission = $575
B) The total sales amount = $20000
Step-by-step explanation:
<h3><u>Part A </u></h3>Given:
Total amount earned = $8,000 in sales
To Find :
The amount of commission, in dollars
Solution:
The commission she earns = Commission 1+ Commission 2----------(1)
Commission 1 = 5% of 5000
Commission 2 = 7.5 % of (8000- 5000}
Finding commission 1:
= 5% of 5000
=
=
= $250 ------------------------------(2)
Finding commission 2:
= 7.5 % of (3000)
=
=
= $225----------------------------------(3)
Substituting (2) and (3) in (1)
The commission she earns = $250 + $225 = $575
<h3><u>Part B</u></h3>Given:
Total commission earned = $1375
To Find :
The total sales amount = ?
Solution ;
Let the sales amount be x
Then
1375 = 5% of 5000 + 7.5 % of (x -5000)
1375 = 250 + 0.075x - 375
1375 = -125 + 0.075 x
1375 +125 = 0.075 x
1500 = 0.075x
x = 20000
The total sales amount is $20000
The denominator( s ) we are given are , and . The first thing we want to do is factor the expressions, to make this easier -
This expression is a perfect square, as ( x )^2 = x^2, ( 2 )^2 = 4, 2 * ( x ) * ( 2 ) = 4x. Thus, the simplified expression should be the following -
The other expression is, on the other hand, not a perfect square so we must break this expression into groups and attempt factorization -
Combining ( x + 2 )^2 and ( x + 2 )( x + 3 ), the expression that contains factors of each is ( x + 2 )^2 * ( x + 3 ), or in other words the LCM.
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