Math / Algebra

Question68. The top three oil producers in the United States in a certain year are the Gulf of Mexico, Texas, and Alaska. The three regions were responsible for $64 \%$ of the United States oil production. The Gulf of Mexico and Texas combined for $47 \%$ of oil production. Texas produced $3 \%$ more than Alaska. What percent of United States oil production came from these regions? ${ }^{4}$

Studdy Solution

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%}!

STEP 12

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.

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Studdy Solution

STEP 1

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%}!

STEP 12

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.

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Studdy Solution

STEP 1

STEP 2

1. Set up variables2. Use the given information3. Solve for Alaska's production4. Solve for Texas's production5. Solve for Gulf of Mexico's production

STEP 3

Let's give these oil-producing giants some snappy variable names!Let ggg be the percentage of oil produced by the Gulf of Mexico, ttt be the percentage produced by Texas, and aaa 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.g + t + a = 64.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.g + t = 47.g+t=47.

STEP 6

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

STEP 7

Let's substitute the second equation, g+t=47g + t = 47g+t=47, into the first equation, g+t+a=64g + t + a = 64g+t+a=64.This gives us 47+a=6447 + a = 6447+a=64.

STEP 8

Subtracting 474747 from both sides of 47+a=6447 + a = 6447+a=64 gives us a=64−47a = 64 - 47a=64−47, so a=17a = 17a=17.Alaska produced \text{17%} of the US oil!

STEP 9

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

STEP 10

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

STEP 11

Subtracting 202020 from both sides of g+20=47g + 20 = 47g+20=47 gives us g=47−20g = 47 - 20g=47−20, so g=27g = 27g=27.The Gulf of Mexico produced \text{27%}!

STEP 12

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%27 + 20 + 17 = 64\%27+20+17=64% of the total US oil production.

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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

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.

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

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

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

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

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!

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%}!

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

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.