Problem Solving with Two-Step Equations Quick Check
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Question
Maria opens a savings account with $50 and then saves $19 each week. How many weeks will it take for her account to reach $259? Represent this problem with an equation in the form px+q=r .(1 point)
Responses
259+50=19x
259 plus 50 equals 19 x
19x−50=259
19 x minus 50 equals 259
50x+19=259
50 x plus 19 equals 259
19x+50=259
19 x plus 50 equals 259
Annette’s soccer team will play 15 games this season. That is 7 games fewer than 2 times the number of games they played last season. How many games did they play last season? Represent this problem with an equation in the form px+q=r .(1 point)
Responses
2x+7=15
2 x plus 7 equals 15
15−7=2x
15 minus 7 equals 2 x
2x−7=15
2 x minus 7 equals 15
7−2x=15
7 minus 2 x equals 15
Solve the following real-world problem: Destiny opens a checking account with $100 and then deposits $27 each week. How many weeks will it take for her account to reach $343? (1 point)
Responses
12.7 weeks
12.7 weeks
3.16 weeks
3.16 weeks
9 weeks
9 weeks
16.4 weeks
We can represent this problem with an equation in the form px + q = r, where p represents the amount deposited each week, x represents the number of weeks, and r represents the target amount in the account.
In this problem, p = 27, q = 100, and r = 343. We want to find the value of x.
So the equation becomes 27x + 100 = 343.
To solve for x, we can subtract 100 from both sides of the equation: 27x = 243.
Then, we divide both sides of the equation by 27: x = 9.
Therefore, it will take Destiny 9 weeks for her account to reach $343.
Solve the following real-world problem: Ahmadullah’s basketball team will play 21 games this season. That is 12 games more than 13 the number of games they played last season. How many games did they play last season?(1 point)
Responses
33 games
33 games
11 games
11 games
7 games
7 games
27 games
We can represent this problem with an equation in the form px + q = r, where p represents the difference in the number of games, x represents the number of games played last season, and r represents the number of games played this season.
In this problem, p = 12, x represents the number of games played last season, and r = 21. We want to find the value of x.
So the equation becomes 13x + 12 = 21.
To solve for x, we can subtract 12 from both sides of the equation: 13x = 9.
Then, we divide both sides of the equation by 13: x = 9/13.
Therefore, Ahmadullah's basketball team played approximately 0.69 games last season. Since we can't have a fraction of a game, we can round up to 1 game.
Therefore, Ahmadullah's basketball team played 1 game last season.
Solve the following real-world problem: Ahmadullah’s basketball team will play 21 games this season. That is 12 games more than 1/3 the number of games they played last season. How many games did they play last season?
33 games
11 games
7 games
27 games
We can represent this problem with an equation in the form px + q = r, where p represents the difference in the number of games, x represents the number of games played last season, and r represents the number of games played this season.
In this problem, p = 12, x represents the number of games played last season, and r = 21. We want to find the value of x.
We are given that this season, the team will play 12 games more than 1/3 the number of games they played last season. Mathematically, this can be represented as:
21 = (1/3)x + 12
To solve for x, we can subtract 12 from both sides of the equation: (1/3)x = 21 - 12 = 9.
Next, we multiply both sides of the equation by 3 to isolate x: 3 * (1/3)x = 3 * 9.
This simplifies to x = 27.
Therefore, Ahmadullah's basketball team played 27 games last season. The correct answer is 27 games.