Math / Algebra

Question10.1: Games and Rides
Jada has $\$ 20$ to spend on games and rides at a carnival. Games cost $\$ 1$ each and rides are \ $2 each.<br />1. Which equation represents the relationship between the number of games,$ x $, and the number of rides,$ y $, that Jada could do if she spends all her money?$ A: x+y=20B: 2 x+y=20 $C:$ x+2 y=20$
2. Explain what each of the other two equations could mean in this situation. 10.2: Graphing Games and Rides ( 30 min )
Here are the three equations. Each represents the relationship between the number of games, $x$ , the number of rides, $y$ , and the dollar amount a student is spending on games and rides at a different amusement park.
Equation $1: x+y=20$ Equation $2: 250 x+y=15$ Equation $3: x+4 y=28$
Your teacher will assign to you (or ask you to choose) 1-2 equations. For each assigned (or chosen) equation, answer the questions.

Studdy Solution

STEP 1

What is this asking? We need to figure out which equation shows how many games and rides Jada can go on with $\$20$ , and then explain what the other equations could mean. Watch out! Don't mix up the cost of games and rides!

STEP 2

1. Find the Right Equation
2. Explore Other Equations

STEP 3

Alright, so Jada has $\$20$ burning a hole in her pocket!
Games are $\$1$ each, and rides are $\$2$ .
Let's use $x$ for the number of games and $y$ for the number of rides.

STEP 4

If Jada plays $x$ games, she spends $1 \cdot x$ dollars, or just $x$ dollars.
If she goes on $y$ rides, that's $2 \cdot y$ dollars, or $2y$ dollars.

STEP 5

Since she's spending all her $\$20$ , the total cost of games plus the total cost of rides has to equal $\$20$ .
So, our equation is $x + 2y = 20$ .
That's option C!

STEP 6

Now, let's see what the other equations could mean.
Equation A is $x + y = 20$ .
This would mean each game and each ride costs the same.
Since the total is still $\$20$ , each game and each ride would cost $\$1$ .

STEP 7

Equation B is $2x + y = 20$ .
This time, the games cost $\$2$ each (notice the $2x$ ), and the rides cost $\$1$ each.
It's like the first scenario, but the prices are swapped!

STEP 8

1. The correct equation is C: $x + 2y = 20$ .
2. Equation A ( $x + y = 20$ ) could mean both games and rides cost $\$1$ .
Equation B ( $2x + y = 20$ ) could mean games cost $\$2$ and rides cost $\$1$ .

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Studdy Solution

STEP 1

What is this asking? We need to figure out which equation shows how many games and rides Jada can go on with $\$20$ , and then explain what the other equations could mean. Watch out! Don't mix up the cost of games and rides!

STEP 2

1. Find the Right Equation
2. Explore Other Equations

STEP 3

Alright, so Jada has $\$20$ burning a hole in her pocket!
Games are $\$1$ each, and rides are $\$2$ .
Let's use $x$ for the number of games and $y$ for the number of rides.

STEP 4

If Jada plays $x$ games, she spends $1 \cdot x$ dollars, or just $x$ dollars.
If she goes on $y$ rides, that's $2 \cdot y$ dollars, or $2y$ dollars.

STEP 5

Since she's spending all her $\$20$ , the total cost of games plus the total cost of rides has to equal $\$20$ .
So, our equation is $x + 2y = 20$ .
That's option C!

STEP 6

Now, let's see what the other equations could mean.
Equation A is $x + y = 20$ .
This would mean each game and each ride costs the same.
Since the total is still $\$20$ , each game and each ride would cost $\$1$ .

STEP 7

Equation B is $2x + y = 20$ .
This time, the games cost $\$2$ each (notice the $2x$ ), and the rides cost $\$1$ each.
It's like the first scenario, but the prices are swapped!

STEP 8

1. The correct equation is C: $x + 2y = 20$ .
2. Equation A ( $x + y = 20$ ) could mean both games and rides cost $\$1$ .
Equation B ( $2x + y = 20$ ) could mean games cost $\$2$ and rides cost $\$1$ .

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Studdy Solution

STEP 1

What is this asking? We need to figure out which equation shows how many games and rides Jada can go on with $20\$20$20, and then explain what the other equations could mean. Watch out! Don't mix up the cost of games and rides!

STEP 2

1. Find the Right Equation2. Explore Other Equations

STEP 3

Alright, so Jada has $20\$20$20 burning a hole in her pocket!Games are $1\$1$1 each, and rides are $2\$2$2.Let's use xxx for the number of games and yyy for the number of rides.

STEP 4

If Jada plays xxx games, she spends 1⋅x1 \cdot x1⋅x dollars, or just xxx dollars.If she goes on yyy rides, that's 2⋅y2 \cdot y2⋅y dollars, or 2y2y2y dollars.

STEP 5

Since she's spending *all* her $20\$20$20, the **total cost** of games plus the **total cost** of rides has to equal $20\$20$20.So, our equation is x+2y=20x + 2y = 20x+2y=20.That's option C!

STEP 6

Now, let's see what the other equations could mean.Equation A is x+y=20x + y = 20x+y=20.This would mean each game *and* each ride costs the same.Since the total is still $20\$20$20, each game and each ride would cost $1\$1$1.

STEP 7

Equation B is 2x+y=202x + y = 202x+y=20.This time, the games cost $2\$2$2 each (notice the 2x2x2x), and the rides cost $1\$1$1 each.It's like the first scenario, but the prices are swapped!

STEP 8

1. The correct equation is C: x+2y=20x + 2y = 20x+2y=20.2. Equation A (x+y=20x + y = 20x+y=20) could mean both games and rides cost $1\$1$1.Equation B (2x+y=202x + y = 202x+y=20) could mean games cost $2\$2$2 and rides cost $1\$1$1.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to figure out which equation shows how many games and rides Jada can go on with $\$20$ , and then explain what the other equations could mean. Watch out! Don't mix up the cost of games and rides!

1. Find the Right Equation
2. Explore Other Equations

Alright, so Jada has $\$20$ burning a hole in her pocket!
Games are $\$1$ each, and rides are $\$2$ .
Let's use $x$ for the number of games and $y$ for the number of rides.

If Jada plays $x$ games, she spends $1 \cdot x$ dollars, or just $x$ dollars.
If she goes on $y$ rides, that's $2 \cdot y$ dollars, or $2y$ dollars.

Since she's spending all her $\$20$ , the total cost of games plus the total cost of rides has to equal $\$20$ .
So, our equation is $x + 2y = 20$ .
That's option C!

Now, let's see what the other equations could mean.
Equation A is $x + y = 20$ .
This would mean each game and each ride costs the same.
Since the total is still $\$20$ , each game and each ride would cost $\$1$ .

Equation B is $2x + y = 20$ .
This time, the games cost $\$2$ each (notice the $2x$ ), and the rides cost $\$1$ each.
It's like the first scenario, but the prices are swapped!

1. The correct equation is C: $x + 2y = 20$ .
2. Equation A ( $x + y = 20$ ) could mean both games and rides cost $\$1$ .
Equation B ( $2x + y = 20$ ) could mean games cost $\$2$ and rides cost $\$1$ .