QuestionFind the year when income $y$ reaches 728.34 billion using the equation $112.4(x-2010)=7y-3749.58$ . What is $y$ ?

Studdy Solution

STEP 1

Assumptions1. The equation given is valid and describes the relationship between the year and the income taken in by the social security administration. . The trend described by the equation continues into the future.
3. The value of $y$ we are looking for is728.34 (in billions of dollars).

STEP 2

We are given the equation $112.4(x-2010)=7 y-3749.58$ and we are asked to find the year $x$ when $y=728.34$ .

STEP 3

First, we substitute $y=728.34$ into the equation.
$112.(x-2010)=7 \times728.34-3749.58$

STEP 4

Next, we simplify the right-hand side of the equation.
$112.4(x-2010)=5098.38-3749.58$

STEP 5

We continue to simplify the right-hand side of the equation.
$112.4(x-2010)=1348.8$

STEP 6

Next, we isolate $x$ by dividing both sides of the equation by112.4.
$x-2010=\frac{1348.8}{112.4}$

STEP 7

We calculate the right-hand side of the equation.
$x-2010=12$

STEP 8

Finally, we solve for $x$ by adding2010 to both sides of the equation.
$x=2010+12$

STEP 9

We calculate the value of $x$ .
$x=2022$ In the year2022,728.34 billion dollars will be taken in.

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QuestionFind the year when income $y$ reaches 728.34 billion using the equation $112.4(x-2010)=7y-3749.58$ . What is $y$ ?

Studdy Solution

STEP 1

Assumptions1. The equation given is valid and describes the relationship between the year and the income taken in by the social security administration. . The trend described by the equation continues into the future.
3. The value of $y$ we are looking for is728.34 (in billions of dollars).

STEP 2

We are given the equation $112.4(x-2010)=7 y-3749.58$ and we are asked to find the year $x$ when $y=728.34$ .

STEP 3

First, we substitute $y=728.34$ into the equation.
$112.(x-2010)=7 \times728.34-3749.58$

STEP 4

Next, we simplify the right-hand side of the equation.
$112.4(x-2010)=5098.38-3749.58$

STEP 5

We continue to simplify the right-hand side of the equation.
$112.4(x-2010)=1348.8$

STEP 6

Next, we isolate $x$ by dividing both sides of the equation by112.4.
$x-2010=\frac{1348.8}{112.4}$

STEP 7

We calculate the right-hand side of the equation.
$x-2010=12$

STEP 8

Finally, we solve for $x$ by adding2010 to both sides of the equation.
$x=2010+12$

STEP 9

We calculate the value of $x$ .
$x=2022$ In the year2022,728.34 billion dollars will be taken in.

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QuestionFind the year when income yyy reaches 728.34 billion using the equation 112.4(x−2010)=7y−3749.58112.4(x-2010)=7y-3749.58112.4(x−2010)=7y−3749.58. What is yyy?

Studdy Solution

STEP 1

Assumptions1. The equation given is valid and describes the relationship between the year and the income taken in by the social security administration. . The trend described by the equation continues into the future.3. The value of yyy we are looking for is728.34 (in billions of dollars).

STEP 2

We are given the equation112.4(x−2010)=7y−3749.58112.4(x-2010)=7 y-3749.58112.4(x−2010)=7y−3749.58and we are asked to find the year xxx when y=728.34y=728.34y=728.34.

STEP 3

First, we substitute y=728.34y=728.34y=728.34 into the equation.112.(x−2010)=7×728.34−3749.58112.(x-2010)=7 \times728.34-3749.58112.(x−2010)=7×728.34−3749.58

STEP 4

Next, we simplify the right-hand side of the equation.112.4(x−2010)=5098.38−3749.58112.4(x-2010)=5098.38-3749.58112.4(x−2010)=5098.38−3749.58

STEP 5

We continue to simplify the right-hand side of the equation.112.4(x−2010)=1348.8112.4(x-2010)=1348.8112.4(x−2010)=1348.8

STEP 6

Next, we isolate xxx by dividing both sides of the equation by112.4.x−2010=1348.8112.4x-2010=\frac{1348.8}{112.4} x−2010=112.41348.8​

STEP 7

We calculate the right-hand side of the equation.x−2010=12x-2010=12x−2010=12

STEP 8

Finally, we solve for xxx by adding2010 to both sides of the equation.x=2010+12x=2010+12x=2010+12

STEP 9

We calculate the value of xxx.x=2022x=2022x=2022In the year2022,728.34 billion dollars will be taken in.

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Studdy solves anything!

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QuestionFind the year when income $y$ reaches 728.34 billion using the equation $112.4(x-2010)=7y-3749.58$ . What is $y$ ?

Assumptions1. The equation given is valid and describes the relationship between the year and the income taken in by the social security administration. . The trend described by the equation continues into the future.
3. The value of $y$ we are looking for is728.34 (in billions of dollars).

We are given the equation $112.4(x-2010)=7 y-3749.58$ and we are asked to find the year $x$ when $y=728.34$ .

First, we substitute $y=728.34$ into the equation.
$112.(x-2010)=7 \times728.34-3749.58$

Next, we simplify the right-hand side of the equation.
$112.4(x-2010)=5098.38-3749.58$

We continue to simplify the right-hand side of the equation.
$112.4(x-2010)=1348.8$

Next, we isolate $x$ by dividing both sides of the equation by112.4.
$x-2010=\frac{1348.8}{112.4}$

We calculate the right-hand side of the equation.
$x-2010=12$

Finally, we solve for $x$ by adding2010 to both sides of the equation.
$x=2010+12$

We calculate the value of $x$ .
$x=2022$ In the year2022,728.34 billion dollars will be taken in.