Math Snap

STEP 1

What is this asking?
How much oil did the Gulf of Mexico, Texas, and Alaska each produce, if together they made \text{64%} of the total US oil production, and we know some relationships between their production levels?
Watch out!
Don't mix up percentages with actual amounts.
We're dealing with percentages of the total US oil production here.

STEP 2

1. Set up variables
2. Use the given information
3. Solve for Alaska's production
4. Solve for Texas's production
5. Solve for Gulf of Mexico's production

STEP 3

Let's give these oil-producing giants some snappy variable names!
Let $g$ be the percentage of oil produced by the Gulf of Mexico, $t$ be the percentage produced by Texas, and $a$ be the percentage produced by Alaska.

STEP 4

We know that together, these three regions produced \text{64%} of the US oil production.
This gives us our first equation:
$$g + t + a = 64.$$

STEP 5

We also know the Gulf of Mexico and Texas combined for \text{47%}.
That's equation number two:
$$g + t = 47.$$

STEP 6

Finally, Texas produced \text{3%} more than Alaska.
Mathematically, this translates to:
$$t = a + 3.$$

STEP 7

Let's substitute the second equation, $g + t = 47$, into the first equation, $g + t + a = 64$.
This gives us $47 + a = 64$.

STEP 8

Subtracting $47$ from both sides of $47 + a = 64$ gives us $a = 64 - 47$, so $a = 17$.
Alaska produced \text{17%} of the US oil!

STEP 9

Now that we know Alaska's production, we can plug $a = 17$ into the equation $t = a + 3$.
This gives us $t = 17 + 3$, so $t = 20$.
Texas produced \text{20%}!

STEP 10

We know $g + t = 47$, and we just found out $t = 20$.
Substituting, we get $g + 20 = 47$.

STEP 11

Subtracting $20$ from both sides of $g + 20 = 47$ gives us $g = 47 - 20$, so $g = 27$.
The Gulf of Mexico produced \text{27%}!

The Gulf of Mexico produced \text{27%}, Texas produced \text{20%}, and Alaska produced \text{17%} of the US oil production in that year.
Together, that's $27 + 20 + 17 = 64\%$ of the total US oil production.