A real estate salesperson bought promotional calendars and date books to give to her customers at the end of the year. The calendars cost $0.75 each, and the date books cost $0.40 each. She ordered a total of 600 promotional items and spent $380. How many of each item did she order?
Ms. Sue, would you mind assisting me with this math problem?
Let c be the number of calender, and d be the number of datebooks.
The total number of items tells us that:
c + d = 600
Rearranging:
d = 600 - c
The total cost tells us that:
0.76 c + 0.40 d = 380
Substituting d = 600 - c:
0.75 c + 0.40 (600 - c) = 380
Simplify to solve for c:
...
c = ___
Use d = 600 - c to find d:
d = ___
Concluding:
c=___ calenders at $0.75ea and d=___ date books at $0.40ea, are 600 items that costs $380 in total.
Thank you Graham
To determine the number of calendars and date books the salesperson ordered, let's set up a system of equations based on the given information.
Let's assume the salesperson bought x calendars and y date books.
The cost of each calendar is $0.75, so the total cost of the calendars is 0.75x.
The cost of each date book is $0.40, so the total cost of the date books is 0.40y.
According to the given information, the salesperson ordered a total of 600 promotional items and spent $380. Therefore, we can write the following equations:
x + y = 600 (equation 1, as the total number of items is 600)
0.75x + 0.40y = 380 (equation 2, as the total cost is $380)
Now, we can solve this system of equations.
First, let's simplify equation 2 by multiplying each term by 100 to get rid of the decimal:
75x + 40y = 38000
Now, let's solve this system of equations using the method of substitution.
From equation 1, we have x = 600 - y.
Substituting this value of x into equation 2, we get:
75(600 - y) + 40y = 38000
45000 - 75y + 40y = 38000
Combine like terms:
-35y = -7000
Divide by -35:
y = 200
Substituting this value of y back into equation 1, we find:
x + 200 = 600
x = 400
Therefore, the salesperson ordered 400 calendars and 200 date books.