Algebraic Word Problem involving calcium and Vit A and orange juice. HELP!!!

[Steph Annie]

Hi, can someone help me with this algebraic word problem? It is a real headache. Thanks!

"Pat wants to increase his daily intake of calcium to 500 milligrams, and his intake of Vit A to 1200 micrograms. If one ounce of milk has 37 mg of calcium, and 57 micrograms of Vit A, and once ounce of orage juice contains 5 mg of calcium, and 65 micrograms of Vit A, how much of each should Pat drink to meet his goal?"

 

[soroban]

Hello, Steph Annie!

Pat wants to increase his daily intake of Calcium to 500 milligrams,
. . and his intake of Vitamin A to 1200 micrograms.
One ounce of milk has 37 mg of Calcium and 57 micrograms of Vitamin A.
One ounce of orange juice has 5 mg of Calcium and 65 micrograms of Vitamin A.
How much of each should Pat drink to meet his goal?

Let \(\displaystyle x\) = ounces of milk.
Let \(\displaystyle y\) = ounces of O.J.

. . \(\displaystyle \begin{array}{c|c|c|} & \text{Calcium} & \text{Vit.A} \\ & \text{(mg)} & (\mu\text{g}) \\ \hline \text{Milk }(x) & 37x & 57x \\ \hline \text{O.J. }(y) & 5y & 65y \\ \hline \text{Total} & 500 & 1200 \\ \hline \end{array}\)


Read down the columns: .\(\displaystyle \begin{Bmatrix}37x + 5y &=& 500 \\ 57x + 65y &=& 1200 \end{Bmatrix}\)

Solve the system of equations.