Question

Dave receives a salary of $200 a week plus a commission of 10% of his weekly sales. An equation y=mx+b represents Dave’s weekly earnings. The y-intercept is Dave’s base salary. The slope of the line is his commission. Write an equation representing Dave’s weekly earnings. If Dave sells $1500 of goods for one week, what is his salary for the week? a. $13,000 b. $350 c. $1520 d. $130

Answer 1

`y=0.10x+200`

b. $350

Step-by-step explanation:

Let x represent the cost of goods sold by Dave.

We have been given that Dave receives a salary of $200 a week plus a commission of 10% of his weekly sales.

We are asked to write an equation that represents Dave’s weekly earnings in slope-intercept form of equation, where, y-intercept is Dave’s base salary and the slope of the line is his commission.

We know that slope-intercept form of an equation is in format:
`y=mx+b`, where,

m = Slope of line,

b = The y-intercept.

As we have been given that y-intercept is Dave’s base salary, so this means that value of b is 200.

Now, we need to find the slope of our line.

The slope of line will be Dave's commission. This means that slope of line will be 10% of x.

`\text{10\% of x}=(10)/(100)x=0.10x`

Upon substituting our given values in slope-intercept form of equation we will get,

`y=0.10x+200`

Therefore, the equation
`y=0.10x+200` represents Dave's weekly earnings.

To find Dave's salary we need to substitute
`x=1500` in our given equation.

`y=0.10\cdot 1500+200`

`y=150+200`

`y=350`

Therefore, Dave's weekly salary for the week is $350 and option 'b' is the correct choice.

Answer 2

Answer:
Dave makes $350

Step-by-step explanation:
In order to find this answer, we must first establish the equation for his earnings.
We use slope intercept form:
y = mx + b,
where m = slope and b = y-intercept.

Since the problem states that his commission percentage is the slope and his base salary is the y-intercept, we can use them in the equation to get the following:
y = 0.1x + 200.

Now knowing that the x is the amount he sells, we can use the $1500 as x to find his total pay for the week:.
y = 0.1(1500) + 200,
y = 150 + 200,
y = 350.