01.12.2022

The Groves basketball team did not record how many baskets were made by each player during the last game. Daniel remembers that he made three times as many baskets as Ben. Max knows that he made six more baskets than Ben. Mitchell is sure that he made fewer baskets than Ben. Christion is sure that he made the same number of baskets as Mitchell. Altogether the five players made 40 baskets. How many baskets did each player make?

. 0

Step-by-step answer

24.06.2023, solved by verified expert
Unlock the full answer
1 students found this answer . helpful

Answers:

Ben = 6Max = 12Mitchell = 2Christion = 2Daniel = 18

Each count above refers to the number of baskets made for the given player.

Explanation:

For each player, let the following variables represent how many baskets were made

B = BenM = MaxT = MitchelC = ChristionD = Daniel

So for example, if D = 10, then this means Daniel made 10 baskets. Though for now, we're not sure what number replaces D or any given letter.

"Daniel remembers that he made three times as many baskets as Ben" tells us that D = 3B is one equation

We know another equation is M = B+6 since Max made six more baskets than Ben

Another equation is C = T because these two students (Christion and Mitchell) made the same number of baskets.

We also know that T < B since Mitchell made fewer baskets compared to Ben.

Altogether the boys made 40 baskets total, so B+M+T+C+D = 40

We have these five mathematical statements

D = 3BM = B+6C = TT < BB+M+T+C+D = 40

Let's focus on the last equation

B+M+T+C+D = 40

B+M+T+C+3B = 40 plug in D = 3B

4B+M+T+C = 40

4B+M+T+T = 40 plug in C = T

4B+M+2T = 40

4B+B+6+2T = 40 plug in M = B+6

5B+6+2T = 40

5B+2T = 40-6

5B+2T = 34

Now let's solve for T

5B+2T = 34

2T = 34-5B

2T = -5B+34

T = (-5B+34)/2

T = (-5B)/2 + 34/2

T = -2.5B + 17

We've eliminated everything but two variables at this point.

Let's say that x replaced B and y replaces T

We get the equation y = -2.5x + 17

If you graph this equation along with y = x, you'll find that the two equations intersect at roughly (4.857, 4.857)

Since we want T < B, this means we want y < x to be the case. The line y = -2.5x+17 goes downhill as we move from left to right. If x is smaller than 4.857, then x >= y. Otherwise, if x is larger than 4.857, then y < x

Furthermore, looking at a table of values for this equation shows that only (x,y) = (6,2) is a point on y = -2.5x+17 such that both x and y are positive and x is the larger value, and they are both integer coordinates.

All of this means that when B = 6, this pairs with T = 2. No other number pair is possible for these two students.

We then use this to find the other player's basket count

D = 3B = 3*6 = 18M = B+6 = 6+6 = 12C = T = 2

So we have the following results

B = 6M = 12T = 2C = 2D = 18

As a check,

B+M+T+C+D = 6+12+2+2+18 = 40

which confirms our answers.

It is was helpful?
Unlock the full answer
1 students found this answer . helpful

9514 1404 393

Ben: 6Daniel: 18Max: 12Mitchell: 2Christion: 2

Step-by-step explanation:

Let x and y represent baskets made by Ben and Mitchell, respectively. Then Daniel made 3x baskets, Max made (x+6) baskets, and Christion made y baskets. The total number is ...

  x + 3x +(x+6) +y +y = 40

  5x +2y = 34 . . . . . . . . . . . subtract 6

The other constraint on the solution is ...

  y < x . . . . . . . . . Mitchell made fewer baskets than Ben

__

We can see that 34 differs from a multiple of 5 by an even number, so (by inspection) we determine that (x, y) = (6, 2) is a solution to the equation. (It is also a solution to the inequality.)

Other possible solutions will require y increase by 5 as x decreases by 2, so those are ...

  (x, y) = {(6, 2), (4, 7), (2, 12), (0, 17)}

The only (x, y) pair that satisfies the inequality is the first one: (x, y) = (6, 2). Hence the numbers of baskets are ...

Ben: 6Daniel: 18Max: 12Mitchell: 2Christion: 2
The Groves basketball team did not record how, №17886314, 01.12.2022 02:35
It is was helpful?

Faq

Mathematics
Step-by-step answer
P Answered by PhD

Answers:

Ben = 6Max = 12Mitchell = 2Christion = 2Daniel = 18

Each count above refers to the number of baskets made for the given player.

Explanation:

For each player, let the following variables represent how many baskets were made

B = BenM = MaxT = MitchelC = ChristionD = Daniel

So for example, if D = 10, then this means Daniel made 10 baskets. Though for now, we're not sure what number replaces D or any given letter.

"Daniel remembers that he made three times as many baskets as Ben" tells us that D = 3B is one equation

We know another equation is M = B+6 since Max made six more baskets than Ben

Another equation is C = T because these two students (Christion and Mitchell) made the same number of baskets.

We also know that T < B since Mitchell made fewer baskets compared to Ben.

Altogether the boys made 40 baskets total, so B+M+T+C+D = 40

We have these five mathematical statements

D = 3BM = B+6C = TT < BB+M+T+C+D = 40

Let's focus on the last equation

B+M+T+C+D = 40

B+M+T+C+3B = 40 plug in D = 3B

4B+M+T+C = 40

4B+M+T+T = 40 plug in C = T

4B+M+2T = 40

4B+B+6+2T = 40 plug in M = B+6

5B+6+2T = 40

5B+2T = 40-6

5B+2T = 34

Now let's solve for T

5B+2T = 34

2T = 34-5B

2T = -5B+34

T = (-5B+34)/2

T = (-5B)/2 + 34/2

T = -2.5B + 17

We've eliminated everything but two variables at this point.

Let's say that x replaced B and y replaces T

We get the equation y = -2.5x + 17

If you graph this equation along with y = x, you'll find that the two equations intersect at roughly (4.857, 4.857)

Since we want T < B, this means we want y < x to be the case. The line y = -2.5x+17 goes downhill as we move from left to right. If x is smaller than 4.857, then x >= y. Otherwise, if x is larger than 4.857, then y < x

Furthermore, looking at a table of values for this equation shows that only (x,y) = (6,2) is a point on y = -2.5x+17 such that both x and y are positive and x is the larger value, and they are both integer coordinates.

All of this means that when B = 6, this pairs with T = 2. No other number pair is possible for these two students.

We then use this to find the other player's basket count

D = 3B = 3*6 = 18M = B+6 = 6+6 = 12C = T = 2

So we have the following results

B = 6M = 12T = 2C = 2D = 18

As a check,

B+M+T+C+D = 6+12+2+2+18 = 40

which confirms our answers.

Mathematics
Step-by-step answer
P Answered by PhD
Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram
Mathematics
Step-by-step answer
P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

Mathematics
Step-by-step answer
P Answered by PhD

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

Mathematics
Step-by-step answer
P Answered by PhD
The answer is in the image 

The answer is in the image 

Mathematics
Step-by-step answer
P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Mathematics
Step-by-step answer
P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Approximately it is aqual to 1300kg

Mathematics
Step-by-step answer
P Answered by PhD

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

Try asking the Studen AI a question.

It will provide an instant answer!

FREE