1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Agata [3.3K]
3 years ago
9

The sum of two numbers is 86, and their difference is 20. Find the two numbers

Mathematics
2 answers:
sp2606 [1]3 years ago
7 0

Answer:

x = 53, y = 33

Step-by-step explanation:

Let one of the numbers = x, & the other = y. Set the equations:

x + y = 86

x - y = 20

This is a system of equation, in which the variables must be true for both of them.

First, choose a equation to use. In this case, I will choose x + y = 86. Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract y from both sides.

x + y = 86

x + y (-y) = 86 (-y)

x = 86 - y

Now, note the other equation: x - y = 20. You now know that x = 86 - y. Plug in 86 - y for x in the "other" equation:

x - y = 20

(86 - y) - y = 20

Simplify. Combine like terms:

86 - y - y = 20

86 - 2y = 20

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS (Parenthesis, Exponents (& Roots), Multiplication, Division, Addition, Subtraction):

First, subtract 86 from both sides:

86 (-86) - 2y = 20 (-86)

-2y = 20 - 86

-2y = -66

Isolate the variable, y. Divide -2 from both sides:

(-2y)/-2 = (-66)/-2

<em>Note: Before we go any further, I want to remind you of division & multiplication rules. There are 3 kinds, when you are multiplying two positive numbers (+/+), when you are multiplying a positive number with a negative number (+/-), and when you are multiplying a two negative numbers (-/-)</em>. <em>Note the "table" in the bottom</em>:

________________________________________________________

(+/+) : Two positive numbers multiplied/divided with each other will always result in a positive answer:

Examples:

10/5 = 2

20/10 = 2

(+/-) : One positive number and one negative number multiplied/divided with each other will always result in a negative answer:

Examples:

20 x -5 = -100

50 x -3 = -150

(-/-) : Two negative numbers multiplied/divided with each other will always result in a positive answer:

Examples:

-30 x -5 = 150

-200/-10 = 20

________________________________________________________

Now, solve the equation:

(-2y)/-2 = (-66)/-2

y = -66/-2

Divide.

y = 33

One of your numbers (y) is 33. Plug in 33 for y in one of the equations:

x + y = 86

x + (33) = 86

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 33 from both sides.

x + 33 (-33) = 86 (-33)

x = 86 - 33

x = 53

Your answers: x = 53, y = 33.

Check: Plug in 53 for x, 33 for y in the equations:

<u>x + y = 86:</u>

(53) + (33) = 86

86 = 86 (True)

<u>x - y = 20</u>:

(53) - (33) = 20

20 = 20 (True)

Your answers: x = 53, y = 33

~

<u />

sukhopar [10]3 years ago
3 0

Answer: 53 and 33

Step-by-step explanation:

Let be "x" the first number and "y" the second number.

Based on the information provided we can set up a system of equations:

\left \{ {{x+y=86} \atop {x-y=20}} \right.

Applying the Elimination method, we can add both equations and solve for the variable "x":

\left \{ {{x+y=86} \atop {x-y=20}} \right.\\................\\2x=106\\\\x=\frac{106}{2}\\\\x=53

Now we can substitute x=53 into one of the original equations and solve for the variable "y":

53+y=86\\\\y=86-53\\\\y=33

You might be interested in
Write the equation of a line that goes through the points (-7,10) and (1,4)
Bad White [126]
I’m pretty sure the answer is y=3/4x-13/4
8 0
3 years ago
Read 2 more answers
A bowl is the shape of a hemisphere and made out of thick clay. The diameter of the outside bowl is 44.6 cm. And the diameter of
aleksandr82 [10.1K]

Answer:

Step-by-step explanation:

Ive already explained this somebody else asked if you find it you will have the answer

3 0
3 years ago
I need answer ASAP I have 30 minutes and 3 more questions to answer. SHOW YOUR WORK PLEASE.
Gnom [1K]

Answer:

6 weeks

Step-by-step explanation:

6*5=30

100+30=130

20*6=120

120+10=130

130=130

5 0
2 years ago
The scores for a certain test of intelligence are normally distributed with mean 85 and standard deviation 11. Find the 90th per
jonny [76]

Answer:

99.1 is the 90th percentile of these scores.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 85

Standard Deviation, σ = 11

We are given that the distribution of score is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

We have to find the value of x such that the probability is 0.90

P( X < x) = P( z < \displaystyle\frac{x - 85}{11})=0.90  

Calculation the value from standard normal z table, we have,  

P(z \leq 1.282) = 0.90

Putting values, we get,

\displaystyle\frac{x - 85}{11} = 1.282\\\\x = 99.1

Thus, 99.1 is the 90th percentile of these scores.

5 0
3 years ago
Charles bought 7/8 foot of electrical wire and 5/6 foot of copper wire for his science project .What is the least common denomin
coldgirl [10]

Answer:

The least common denominator of the fractions is 24

Step-by-step explanation:

we know that

The <u>least common denominator</u> (LCD) is the smallest number that can be a common denominator for a set of fractions

so

we have

7/8

Multiples of 8 -------> 8,16,24,32,...

5/6

Multiples of 6 -------> 6,12,18,24,...

24 is a common multiple of 6 and 8.  It is their lowest common multiple

<em>Alternative Method</em>

we have

8=2^{3}

6=2*3

The least common multiple are those common and non-common numbers with the greatest exponent

so

lcm= 2^{3}*3=24

6 0
3 years ago
Other questions:
  • According to cbs money watch, the average monthly household cellular phone bill is $100. suppose monthly household cell phone bi
    8·1 answer
  • What is the area of a triangle with a height of 14 feet and a base of 10 feet​
    5·2 answers
  • 8y-9y , show work even tho i know it’s not a lot !
    15·1 answer
  • Thank you for you're help
    7·1 answer
  • There are 4 generations. Daughter, mother, grandma, and great-grandma. The daughter is 44 less than the grandma's age. The great
    15·1 answer
  • Write the equation of the line, in slope-intercept form, with the
    15·1 answer
  • What is 6.30054 rounded to the nearest thousandth?
    14·2 answers
  • What is a factor of 42
    14·2 answers
  • What multiplies to 18 and sums up to negative 19
    7·1 answer
  • Please Help Me With This Math. It's 4th Grade Math!!!
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!