Keiko is a software saleswoman. Let x represent her total pay (in dollars). Let y represent the number of copies of History is Fun she sells. Suppose that x and y are related by the equation 2200+900x=y.
Answer the questions below.
Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number
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What is the change in Keiko's total pay for each copy of History is Fun she sells?
What is Keiko's total pay if she doesn't sell any copies of History is Fun?
To solve the equation 2200 + 900x = y for x, we need to isolate x. We can do this by rearranging the equation:
900x = y - 2200
Now divide both sides of the equation by 900 to solve for x:
x = (y - 2200) / 900
So, the equation relating x and y is x = (y - 2200) / 900.
Now, let's answer the questions using this equation:
1. What does the number 2200 represent in the equation?
The number 2200 represents a constant term. It is a fixed value that does not change no matter what the value of y is.
2. What does the number 900 represent in the equation?
The number 900 represents the rate at which Keiko earns money for each copy of "History is Fun" she sells. It tells us that for every copy sold, she earns $900.
3. What does the variable x represent?
The variable x represents Keiko's total pay (in dollars). It is the value we want to find.
4. What does the variable y represent?
The variable y represents the number of copies of "History is Fun" Keiko sells. It is the given information in the problem.
5. If Keiko sells 10 copies of "History is Fun", what is her total pay?
To find Keiko's total pay, we substitute y = 10 into the equation:
x = (10 - 2200) / 900
Simplifying, we have:
x = -2190 / 900
x ≈ -2.4333
Keiko's total pay would be approximately -$2.43. Note that the negative sign indicates a decrease or loss in money.
6. If Keiko's total pay is $5000, how many copies of "History is Fun" did she sell?
To find the number of copies sold, we substitute x = $5000 into the equation:
$5000 = (y - 2200) / 900
Now we can solve for y. First, multiply both sides of the equation by 900:
$5000 * 900 = y - 2200
4500000 = y - 2200
Next, isolate y by adding 2200 to both sides of the equation:
y = 4500000 + 2200
y = 4502200
Keiko sold approximately 4,502,200 copies of "History is Fun".
To find the answers to the questions, we need to understand the given equation and its relationship between x (total pay) and y (number of copies sold).
The equation given is: 2200 + 900x = y.
1. How much does Keiko earn if she sells 4 copies of "History is Fun"?
To find Keiko's total pay (x) for selling 4 copies of "History is Fun," we substitute y = 4 into the equation and solve for x.
Replace y with 4:
2200 + 900x = 4
Now, solve for x by isolating it on one side of the equation:
900x = 4 - 2200
900x = -2196
x = -2196 / 900
x ≈ -2.44
Keiko's total pay would be approximately -2.44 dollars if she sells 4 copies of "History is Fun."
2. How many copies of "History is Fun" do you have to sell for your total pay to be $4,000?
To find the number of copies (y) Keiko needs to sell to earn a total pay of $4,000, we substitute x = 4,000 into the equation and solve for y.
Replace x with 4,000:
2200 + 900(4,000) = y
Now, solve for y:
2200 + 3,600,000 = y
3,602,200 = y
Keiko needs to sell approximately 3,602,200 copies of "History is Fun" to earn a total pay of $4,000.
3. If Keiko's total pay increases by $2,700, how many copies of "History is Fun" did she sell?
To find the number of copies (y) Keiko sold when her total pay increased by $2,700, we need to manipulate the equation to determine the change in y.
The original equation: 2200 + 900x = y
Let's represent the increase in total pay by Δx (Δx = 2,700). We want to find Δy (change in copies sold).
Now we have: 2200 + 900x + Δx = y + Δy
Substitute Δx = 2,700 and rearrange the equation:
2200 + 900x + 2,700 = y + Δy
900x + 4,900 = y + Δy
We know that Δy represents the change in copies sold, but we don't know its value yet. Therefore, we cannot determine how many copies Keiko sold when her total pay increased by $2,700 without additional information.
Please note that in the given equation, an increase or decrease in x (total pay) will cause a corresponding increase or decrease in y (number of copies sold) according to the coefficient of x.