MATHEMATICS HIGH SCHOOL

Two teachers, Mr. Meehan and Mrs. Chipps, decide to buy compasses and rulers for their classrooms. Mrs. Chipps buys 30 compasses and 50 rulers for $95. Mr. Meehan buys 40 of each for $116. What are the individual costs of the compasses and rulers that were purchased? Explanation Please

Answers

Answer 1

Answer:

Answer:

compass = $ 2.50 each

ruler = $ 0.40 each

Step-by-step explanation:

Mrs. Chipps buys 30 c + 50 r = $95

Mr. Meehan buys 40 c + 40 r = $116 x (-1.25) to eliminate r

30 c + 50 r = $ 95

-50 c - 50 r = $-145

-20 c = -50

c = 50 / 20

c = $2.5

substitute c = 2.5 into eq. 1

30 c + 50 r = $95

30 (2.5) + 50 r = 95

75 + 50 r = 95

50 r = 95 - 75

r = 20 / 50

r = 0.40

therefore, the individual costs of the compasses and rulers are:

compass = $ 2.50 each

ruler = $ 0.40 each

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Cedric and doug each had an equal amount of money. After cedric spent $35 and doug spent $28, the ratio of cedrics money to dougs money was 2:3. How much money did each boy habe at first?

Answers

Answer:

Each of them had $49 at first.

Step-by-step explanation:

Given:

Cedric and Doug each had an equal amount of money.

Let the number of money they had at first be x

Cedric spent = $35

Doug spent = $28

Cedric Money left = $x-35$

Doug Money left = $x-28$

the ratio of Cedric money to Doug money was 2:3

Hence the expression can be made as;

$(x-35)/(x-28)=(2)/(3)$

Now by cross multiplication method we get;

$3(x-35)=2(x-28)$

Now we will use distributive property to elaborate the same;

$3x-105=2x-56$

Combining common terms we get;

$3x-2x=105-56$

Using Subtraction property we get;

$x= 49$

Hence $49 they each had at first.

-x+y=4 3x-2y=-7 substitution

Answers

-x+y=4 add x to both sides to get y=x+4 Plug x+4 into the equation for y to get 3x-2(x+4)=-7 Distribute to get 3x-2x-8=-7 Add 8 to both sides to get 3x-2x=1 Subtract 3x-2x to get x=1 the answer is 1

Triangle inequality theorem

Answers

The triangle inequality theorem is an important part of geometry in order to mention the dimension of the sides of a triangle clearly.

What is triangle inequality theorem?

The triangle inequality theorem states that, the sum of the length of two sides must be greater than the length of the third side of that triangle.

Here, three sides of this triangle ABC are AB, BC, and CA.

Therefore, as per the triangle inequality theorem:

(Length of AB + length of BC) must be greater than the length of CA.

Therefore, (AB + BC) > CA.

(Length of BC + length of CA) must be greater than the length of AB.

Therefore, (BC + CA) > AB.

(Length of AB + length of CA) must be greater than the length of BC.

Therefore, (AB + CA) > BC

For an example, if we are running in a triangular shaped track, then it can be easily understandable.

Now, if we start running from the point A, then to reach the point B the shortest path will be the straight line AB.

Instead of that, if we go to the C point at first and then reach the point B, then we will travel more distance.

Similarly, starting from the other points, we will get the same results.

Learn more about triangular inequality theorem here: brainly.com/question/18345497

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Triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side because if not you don't have a triangle.

Explain one thing you need to be careful with when writing a proportion.