Jane was given the following advice. She should supplement her daily diet at least 5000 UPS units of Vitamin A, at least 195 mg of Vitamin C, and at least 700 UPS units of Vitamin D. She also finds that Mason's Pharmacy carries Brand X and Brand Y vitamins. Each brand X pill contains 3000 UPS units of A, 45 mg of C, and 75 UPS units of D, while the brand Y contains 1000 UPS units of A, 50 mg of C and 200 UPS units of D. Let x represent the number of brand X pills, and let y represent the number of Brand Y pills. Write the system of inequalities for the problem.
+23254 You can use these:
A ≥ 5000
C ≥ 195
D ≥ 700
x = 3000A + 45C + 75D
y = 1000A + 50C + 200D
However, the direct combination of these equations/inequalities won't give you the answer that you want.
The number of type x pills necessary:
For vitamin A, you would need to take at least 2 type x pills (5000÷3000 = 1.67 --> 2 pills)
For vitamin C, 195 ÷ 45 = 4.33 ---> 5 pills.
For vitamin D, 700 ÷ 75 = 9.33 ---> 10 pills.
You can make a similar analysis for type y pills.
Then, there is the possibility that you can take a combination of x and y pills.
This can get quite complicated.
+23254 You can use these:
A ≥ 5000
C ≥ 195
D ≥ 700
x = 3000A + 45C + 75D
y = 1000A + 50C + 200D
However, the direct combination of these equations/inequalities won't give you the answer that you want.
The number of type x pills necessary:
For vitamin A, you would need to take at least 2 type x pills (5000÷3000 = 1.67 --> 2 pills)
For vitamin C, 195 ÷ 45 = 4.33 ---> 5 pills.
For vitamin D, 700 ÷ 75 = 9.33 ---> 10 pills.
You can make a similar analysis for type y pills.
Then, there is the possibility that you can take a combination of x and y pills.
This can get quite complicated.
