Hank sells furniture and earns $280/week plus 4% commission.
a) Determine the sales that Hank needs to make to meet his weekly
budget requirement of $900.
b) Write an equation for this situation, and use it to verify your
answer for part.
Let x represent earnings and y represent sales.. So would the equation be y= 280 + 0.04x .. if I'm wrong please correct me I'm not sure about this equation.
y=280+0.04x
900 = 280+0.04x
900-280 = 0.04x
620/0.04 = 0.04x/0.04
15500 = x
x = 280 + .04y
Your equation looks better, but it does not meet the explanation of x and y. Maybe there's a typo.
Oh, Hank and his furniture sales! Let's help him out with the math.
a) To meet his weekly budget requirement of $900, Hank's total earnings need to be equal to or greater than $900. Since he earns a base salary of $280/week, we need to determine how much commission he needs to earn on top of that.
Let's represent his commission as 4% of his sales, which can be denoted as 0.04x (where x represents his sales). So, the equation for his total earnings will be:
Total Earnings = Base Salary + Commission
Total Earnings = $280 + 0.04x
To meet his weekly budget requirement, we need to solve the equation: $900 = $280 + 0.04x
b) The equation you provided, y = 280 + 0.04x, is close! However, in this case, we're focused on earnings as our dependent variable, so let's use E instead of y. So, the correct equation for this situation is:
E = 280 + 0.04x
To verify our answer from part a, we can substitute $900 for E in the equation:
900 = 280 + 0.04x
If we solve this equation, we'll find the value of x (sales) needed for Hank to meet his weekly budget requirement.
I hope that clarifies things for you. Remember, if Hank starts juggling furniture to attract customers, he might sell even more!
You're almost correct with the equation. The equation representing Hank's earnings can be written as:
x = 280 + 0.04y
In this equation, x represents Hank's earnings and y represents his sales. The equation implies that Hank's total earnings (x) is equal to his base salary of $280 plus 4% commission (0.04) multiplied by his sales (y).
Now, let's solve part (a) of the question - determining the sales Hank needs to make to meet his weekly budget requirement of $900.
We'll substitute x with 900 in the equation and solve for y:
900 = 280 + 0.04y
Subtracting 280 from both sides of the equation:
900 - 280 = 0.04y
620 = 0.04y
Dividing both sides by 0.04:
y = 620 / 0.04
y = 15500
Therefore, Hank needs to make $15,500 in sales to meet his weekly budget requirement.
To verify this answer, we can substitute the value of y back into the equation:
x = 280 + 0.04(15500)
x = 280 + 620
x = 900
As you can see, by substituting the value of y back into the equation, we get the original budget requirement of $900, validating our answer.
You are very close with your equation! Here's the correct equation:
Let x represent Hank's sales, and y represent his earnings. Hank earns $280/week plus a 4% commission on his sales.
a) To determine the sales that Hank needs to make to meet his weekly budget requirement of $900, we can set up the equation:
280 + 0.04x = 900
Here, 280 represents Hank's base earnings and 0.04x represents the commission he earns based on his sales. 900 represents the total earnings he needs to meet his weekly budget requirement.
b) To use this equation to verify the answer for part a), we can substitute the value of x into the equation and check if we get the correct earnings:
Let's say Hank's sales, x, is $18,000 (please note that this value is just an example).
Substituting x = $18,000 into the equation:
280 + 0.04(18,000) = 280 + 720 = 1000
Since Hank's earnings (1000) are greater than his required budget of $900 in this example, we can conclude that the equation is correct.
Therefore, the correct equation is y = 280 + 0.04x.