A piece of string is 112 inches long. Cory wants to cut it into two pieces so that one piece is three times as long as the other piece. How long will each piece be?
Responses
A 45 inches and 67 inches45 inches and 67 inches
B 55 inches and 57 inches55 inches and 57 inches
C 28 inches and 84 inches28 inches and 84 inches
D 28 inches and 78 inches
The correct answer is C. The longer piece is three times the length of the shorter piece, so let's call the shorter piece x. The longer piece would then be 3x. The sum of the lengths of the two pieces is 112in, so we can set up the equation:
x + 3x = 112
4x = 112
x = 28
The shorter piece is 28 inches long, and the longer piece is 3 times that, which is 3*28 = 84 inches long.
Miguel and Grace started collecting rare coins at the same time. Back then, they had the same number of rare coins. Miguel has been collecting 5 coins each week and he now has 38 coins. Grace has been collecting 3 coins each week and she now has 24 coins. How many rare coins did they have all together when they started collecting?
Responses
A 33
B 66
C 77
D 14
Let's assume that both Miguel and Grace had x number of rare coins when they started collecting.
Miguel has been collecting 5 coins each week, and he now has 38 coins. This means that he has been collecting for (38 - x) / 5 weeks.
Grace has been collecting 3 coins each week, and she now has 24 coins. This means that she has been collecting for (24 - x) / 3 weeks.
Since Miguel and Grace started collecting at the same time, the number of weeks they have been collecting should be the same. Therefore, we can set up the equation:
(38 - x) / 5 = (24 - x) / 3
Simplifying this equation, we get:
3(38 - x) = 5(24 - x)
114 - 3x = 120 - 5x
2x = 6
x = 3
So, Miguel and Grace each had 3 rare coins when they started collecting. Therefore, they had a total of 3 + 3 = 6 rare coins together when they started collecting.
The correct answer is not provided in the options.
Small boxes contain books, and large boxes contain games. Three boxes of games and a box of
books weighs 48 pounds. Three boxes of games and five boxes of books weigh 72 pounds.
Which system of equations can be used to determine b, the mass, in pounds, of one box of books, and g, the mass, in pounds, of one box of games.
Responses
A 3g + b = 48
3g + 5b = 723 g + b = 48 3 g + 5 b = 72
B 3g + b = 48
3g - 5b = 723 g + b = 48 3 g - 5 b = 72
C 3g - b = 48
3g - 5b = 723 g - b = 48 3 g - 5 b = 72
D 3g - b = 48
3g + 5b = 72
The correct answer is C:
3g - b = 48
3g - 5b = 72
Let's break it down:
The first sentence states that three boxes of games and a box of books weigh 48 pounds. We can represent this as:
3g + b = 48
The second sentence states that three boxes of games and five boxes of books weigh 72 pounds. We can represent this as:
3g + 5b = 72
Since we are looking for the system of equations that can be used to determine the mass of one box of books (b) and one box of games (g), the correct option is C.
u sure
I apologize for the confusion in my previous response. You are correct, the correct answer is A:
3g + b = 48
3g + 5b = 72
Thank you for pointing out the mistake, and I apologize for any confusion caused.
Antonio is buying new rims and tires for his SUV. The total cost of the rims and tires is $2300. If the cost of the tires is $200 more than twice as much as the rims, what is the cost of the rims?
Responses
A $1600$1600
B $1000$1000
C $700$700
D $500
Let's assume the cost of the rims is x dollars.
According to the information given, the cost of the tires is $200 more than twice as much as the rims. This can be expressed as 2x + $200.
The total cost of the rims and tires is $2300. We can set up the equation:
x + (2x + $200) = $2300
Combining like terms, we get:
3x + $200 = $2300
Subtracting $200 from both sides, we get:
3x = $2100
Dividing both sides by 3, we get:
x = $700
Therefore, the cost of the rims is $700.
The correct answer is C: $700.