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Gelneren [198K]
4 years ago
7

Harold has 4 classes each School morning each class is 1 hour long and there are 10 minutes between classes the first class star

ts at 8
a.m. at what time does the 4th Class end
Mathematics
1 answer:
Katena32 [7]4 years ago
6 0
Start at 8 a.m

First class and the break
8.00
1.00
-------- +
9.00
0.10
-------- +
9.10

Second class and the break
start at 9.10
9.10
1.00
------- +
10.10
0.10
-------- +
10.20

Third class and the break
start at 10.20
10.20
1.00
--------- +
11.20
0.10
-------- +
11.30

Fourth class (no break)
start at 11.30
11.30
1.00
-------- +
12.30

Fourth class end at 12.30
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Answer

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Help please
Leno4ka [110]
H = hrs she worked
p = phone calls she answered

h x 10 + p x .25 = maggies earnings

Part A
h x 10 + 60 x .25 = 115

Part B
h x 10 + 15 = 115 (multiplied 60 x .25)
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3 years ago
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The Groves basketball team did not record how many baskets were made by each player during the last game. Daniel remembers that
bixtya [17]

Answers:

  • Ben = 6
  • Max = 12
  • Mitchell = 2
  • Christion = 2
  • Daniel = 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 = Ben
  • M = Max
  • T = Mitchel
  • C = Christion
  • D = 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 = 3B
  • M = B+6
  • C = T
  • T < B
  • B+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 = 18
  • M = B+6 = 6+6 = 12
  • C = T = 2

----------------------------------

So we have the following results

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

As a check,

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

which confirms our answers.

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