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3 years ago

The sum of two numbers is 33. Their difference is 23. Find the numbers.

Mathematics

1 answer:

Ipatiy [6.2K]3 years ago

8 0

Answer: The numbers are 28 and 5

Step-by-step explanation: The question gives a set of clues. In the first instance, the addition of two numbers equals 33. Let us assume the two numbers are A and B. What that means is that

A + B = 33.

We shall call this equation 1.

The other clue is given as “their difference is 23.” This can be expressed as

A - B = 23.

We shall call this equation 2.

Now we have a pair of simultaneous equations as follows

A + B = 33 —————-(1)

A - B = 23 —————-(2)

We shall use the substitution method

From equation (1), if we make A the subject of the equation we shall move B to the other side and we’ll have

A = 33 - B

Substitute for the value of A in equation (2)

A - B = 23 now becomes

(33 - B) - B = 23

33 - B - B = 23

33 - 2B = 23

By collecting like terms we now have 33 - 23 = 2B

(Remember that when a positive value crosses to the other side of an equation, it becomes negative, and vice versa)

33 - 23 = 2B

10 = 2B

Divide both sides of the equation by 2

5 = B

If we calculate B as 5

We can substitute for this value into equation 1, which is

A + B = 33

A + 5 = 33

Subtract 5 from both sides of the equation

A + 5 - 5 = 33 - 5

A = 28.

Therefore the numbers are 28 and 5.

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ki77a [65]

Answer:

Please find attached the graph of the relationship between the gallons, g, and cost, C

The relationship between the cost and number of gallons is cost C = $3.25 × Number of gallons, g

Step-by-step explanation:

The given parameters are;

Number of Gallons, g ${}$ Cost, C

6 ${}$ $19.50 ${}$

22 $71.50

From the given coordinates, we generate the graph using Microsoft Excel, as seen in the attached graph

The given coordinates can be used to find the equation of the relationship in point and slope form as follows;

The slope of the the given coordinates are (71.5 - 19.5)/(22 - 6) = 3.25

The equation of the graph in point and slope form is C - 71.5 = 3.25·(g - 22)

C - 71.5 = 3.25·(g - 22)

C = 3.25·g - 3.25 × 22 + 71.5 = 3.25·g - 0

C = 3.25·g

The relationship between the cost and number of gallons is cost C = $3.25 × Number of gallons, g

From the above equation, we have, that the price per gallon is $3.25

7 0

3 years ago

8x/10x-2 equals 5x+3/7x solve for x

Andrews [41]

Answer:

x = $\frac{1}{3}$ & 3

Step-by-step explanation:

$\frac{8x}{10x-2}$ = $\frac{5x+3}{7x}$

Cross multiply:

$\frac{8x}{10x-2}$ = $\frac{5x+3}{7x}$ ⇒ (8x)(7x) = (5x+3)(10x-2)

Simplify both sides:

(8x)(7x) = (5x+3)(10x-2) ⇒ 56x² = 50x²+20x-6

Set equation equal to 0:

56x² = 50x²+20x-6 ⇒ 0 = -6x²+20x-6

Factor the trinomial:

0 = -6x²+20x-6 = (-6x+2)(x-3)

Solve for X:

-6x+2 = 0

-6x = -2

x = $\frac{1}{3}$ ;

x-3 = 0

x = 3;

x = $\frac{1}{3}$ , 3

4 0

3 years ago

WILL MARK BRAINLIEST!! 8x^2-x^2

Black_prince [1.1K]

Answer:

7x^2

Step-by-step explanation:

hope this help's.

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3 years ago

Out of 600 seniors at a local high school, 60% went on the senior trip. At the hotel, one room was reserved for every 4 students

butalik [34]

Given:

Total number of senior students = 600

60% went on the senior trip.

One room was reserved for every 4 students.

To find:

The total number of reserved rooms.

Solution:

60% went on the senior trip from total 600 students. So, number of students who went on tripe is

$600\times \dfrac{60}{100}=360$

Now, one room was reserved for every 4 students. So,

$\text{Required number of rooms}=\dfrac{\text{Number of students who went on tripe}}{\text{Number of students in room}}$

$\text{Required number of rooms}=\dfrac{360}{4}$

$\text{Required number of rooms}=90$

Therefore, the required number of reserved rooms were 90.

4 0

3 years ago

Students get two grades for a test in an introductory psychology course: a letter grade, and a numerical equivalent (weighted va

vlabodo [156]

Answer:

Average grade for this test = 1.85

Step-by-step explanation:

Given that number of students receiving respective grade scores are : 11, 18, 52, 13, 6

Then total number of students = 11 + 18 + 52 + 13 + 6 = 100

Sum score obtained by total students

= 11F + 18D + 52C + 13B + 6A

= 11(0) + 18(1) + 52(2) + 13(3) + 6(4)

= 0 + 18 + 104 + 39 + 24

= 185

Now average grade for this test is given by 185/100 = 1.85

Hence final answer is 1.85.

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4 years ago

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