Question

An ounce of milk contains 20 milligrams of calcium and 60 micrograms of vitamin A. An ounce of orange juice contains 40 milligrams of calcium and 10 micrograms of vitamin A. How many ounces of milk and orange juice should she drink each day to provide exactly 2200 milligrams of calcium and 1100 micrograms of vitamin A?

Answer 1

We have to take 10 ounces of milk and 50 ounces of juice

Solution:

Given that, An ounce of milk contains 20 milligrams of calcium and 60 micrograms of vitamin A.  

An ounce of orange juice contains 40 milligrams of calcium and 10 micrograms of vitamin A.  

Now, let the number of ounces of milk be “m” ounces and number of ounces of juice be “n” ounces.

Then, “m” ounces of milk will have 20m milligrams calcium and 60m microgram  

And “n” ounces of juice will have 40n mg calcium and 10n micrograms of vitamin

Then in total after drinking milk and juice, we will have  

20m + 40n mg calcium and 60m + 10n mg vitamins

From given information.

$\begin{array}{l}{20 m+40 n=2200} \\\\ {m+2 n=110 \rightarrow(1)} \\\\ {60 m+10 n=1100} \\\\ {6 m+n=110 \rightarrow(2)}\end{array}$

Multiply eqn 2 with 2

12m + 2n = 220  --- eqn 3

Now subtract (1) from eqn 3

12m + 2n = 220

m + 2n = 110

(-) ------------------------------------

11m + 0 = 110

11m = 110

m = 10

Then, from eqn (1)

10 + 2n = 110  

2n = 100  

n = 50

Hence, we have to take 10 ounces of milk and 50 ounces of juice.