QuestionOwen and Jamie spent the same total. Owen spent \$13 on food and played 6 games; Jamie spent \$8.50 on food and played 9 games. Find the price of each game.

Studdy Solution

STEP 1

Assumptions1. Owen and Jamie spent the same total amount of money. . Owen spent $13 on food and played6 carnival games.<br />3. Jamie spent$ 8.50 on food and played9 carnival games.
4. All carnival games cost the same.

STEP 2

Let's denote the price of each carnival game as $x$ . Therefore, the total amount of money Owen spent is $13 +6x$ , and the total amount of money Jamie spent is $8.50 +9x$ .

STEP 3

Since Owen and Jamie spent the same total amount of money, we can set up the following equation $13 +6x =8.50 +9x$

STEP 4

To solve for $x$ , we first isolate $x$ terms on one side of the equation. We can do this by subtracting $6x$ from both sides of the equation $13 +6x -6x =8.50 +9x -6x$

STEP 5

implify the equation $13 =8.50 +3x$

STEP 6

Next, isolate $x$ by subtracting $8.50$ from both sides of the equation $13 -8.50 =8.50 +3x -8.50$

STEP 7

implify the equation $4.50 =3x$

STEP 8

Finally, solve for $x$ by dividing both sides of the equation by3 $x =4.50 /3$

STEP 9

Calculate the value of $x$ $x =4.50 /3 = \$.50$ The price of each carnival game is $.50.

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QuestionOwen and Jamie spent the same total. Owen spent \$13 on food and played 6 games; Jamie spent \$8.50 on food and played 9 games. Find the price of each game.

Studdy Solution

STEP 1

Assumptions1. Owen and Jamie spent the same total amount of money. . Owen spent $13 on food and played6 carnival games.<br />3. Jamie spent$ 8.50 on food and played9 carnival games.
4. All carnival games cost the same.

STEP 2

Let's denote the price of each carnival game as $x$ . Therefore, the total amount of money Owen spent is $13 +6x$ , and the total amount of money Jamie spent is $8.50 +9x$ .

STEP 3

Since Owen and Jamie spent the same total amount of money, we can set up the following equation $13 +6x =8.50 +9x$

STEP 4

To solve for $x$ , we first isolate $x$ terms on one side of the equation. We can do this by subtracting $6x$ from both sides of the equation $13 +6x -6x =8.50 +9x -6x$

STEP 5

implify the equation $13 =8.50 +3x$

STEP 6

Next, isolate $x$ by subtracting $8.50$ from both sides of the equation $13 -8.50 =8.50 +3x -8.50$

STEP 7

implify the equation $4.50 =3x$

STEP 8

Finally, solve for $x$ by dividing both sides of the equation by3 $x =4.50 /3$

STEP 9

Calculate the value of $x$ $x =4.50 /3 = \$.50$ The price of each carnival game is $.50.

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QuestionOwen and Jamie spent the same total. Owen spent \$13 on food and played 6 games; Jamie spent \$8.50 on food and played 9 games. Find the price of each game.

Studdy Solution

STEP 1

STEP 2

Let's denote the price of each carnival game as xxx. Therefore, the total amount of money Owen spent is 13+6x13 +6x13+6x, and the total amount of money Jamie spent is 8.50+9x8.50 +9x8.50+9x.

STEP 3

Since Owen and Jamie spent the same total amount of money, we can set up the following equation13+6x=8.50+9x13 +6x =8.50 +9x13+6x=8.50+9x

STEP 4

To solve for xxx, we first isolate xxx terms on one side of the equation. We can do this by subtracting 6x6x6x from both sides of the equation13+6x−6x=8.50+9x−6x13 +6x -6x =8.50 +9x -6x13+6x−6x=8.50+9x−6x

STEP 5

implify the equation13=8.50+3x13 =8.50 +3x13=8.50+3x

STEP 6

Next, isolate xxx by subtracting 8.508.508.50 from both sides of the equation13−8.50=8.50+3x−8.5013 -8.50 =8.50 +3x -8.5013−8.50=8.50+3x−8.50

STEP 7

implify the equation4.50=3x4.50 =3x4.50=3x

STEP 8

Finally, solve for xxx by dividing both sides of the equation by3x=4.50/3x =4.50 /3x=4.50/3

STEP 9

Calculate the value of xxxx=4.50/3=$.50x =4.50 /3 = \$.50x=4.50/3=$.50The price of each carnival game is $.50.

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Let's denote the price of each carnival game as $x$ . Therefore, the total amount of money Owen spent is $13 +6x$ , and the total amount of money Jamie spent is $8.50 +9x$ .

Since Owen and Jamie spent the same total amount of money, we can set up the following equation $13 +6x =8.50 +9x$

To solve for $x$ , we first isolate $x$ terms on one side of the equation. We can do this by subtracting $6x$ from both sides of the equation $13 +6x -6x =8.50 +9x -6x$

implify the equation $13 =8.50 +3x$

Next, isolate $x$ by subtracting $8.50$ from both sides of the equation $13 -8.50 =8.50 +3x -8.50$

implify the equation $4.50 =3x$

Finally, solve for $x$ by dividing both sides of the equation by3 $x =4.50 /3$

Calculate the value of $x$ $x =4.50 /3 = \$.50$ The price of each carnival game is $.50.