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LekaFEV [45]
3 years ago
13

One number is 2 more than 3 times another. their sum is 22. find the numbers.

Mathematics
2 answers:
kramer3 years ago
8 0
This question is asking for the value of two numbers, which we can label as:

#1 = x
(Any value we do not know can be represented with a variable)
#2 = 3x + 2
("2 more" means + 2, and "3 times" means multiply by 3. The "another" is the variable we talked about before. Combining everything we have 3x + 2).

The last piece of information we are given is that the sum of the two numbers is 22. The word sum indicates that we need to add the two numbers, and when they added they will equal the integer 22.
(x) + (3x + 2) = 22
x + 3x + 2 = 22
Combine like terms
4x + 2 = 22
Subtract 2 from both sides
4x = 20
Divide 4 from both sides
x = 5

This sole value of "x" already gives us the value of the first number. Since our second number is "3x + 2", all we have to do is plug in the value of x into the expression.

3x + 2 = 3(5) + 2 = 15 + 2 = 17
The second number is 17.

Final Answer: The two numbers are 5 and 17.
(If you want to check, add the two numbers and make sure they add up to 22 and multiply 5 by 3 and add 2.)

viktelen [127]3 years ago
4 0
X+3x+2=22
4x=20
x=5
3x+2=17
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45 dimes and 93 nickels were in bank

<em><u>Solution:</u></em>

Let "n" be the number of nickels

Let "d" be the number of dimes

We know that,

value of 1 nickel = $ 0.05

value of 1 dime = $ 0.10

<em><u>Given that There are three more than twice as many nickels as there are dimes</u></em>

Number of nickels = 3 + 2(number of dimes)

n = 3 + 2d ---- eqn 1

<em><u>Also given that coin bank that excepts only nickels and dimes contains $9.15</u></em>

number of nickels x value of 1 nickel + number of dimes x value of 1 dime = 9.15

n \times 0.05 + d \times 0.10 = 9.15

0.05n + 0.10d = 9.15  ---- eqn 2

<em><u>Let us solve eqn 1 and eqn 2</u></em>

Substitute eqn 1 in eqn 2

0.05(3 + 2d) + 0.10d = 9.15

0.15 + 0.1d + 0.10d = 9.15

0.2d = 9

<h3>d = 45</h3>

From eqn 1

n = 3 + 2(45)

n = 3 + 90 = 93

<h3>n = 93</h3>

Thus 45 dimes and 93 nickels were in bank

3 0
3 years ago
What is the correct expansion of the binomial (x+y)^5
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The number 0.8 can be written as 8 over 10, so it is an irrational number, true or false?!?!
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According to an article in Newsweek, the rate of water pollution in China is more than twice that measured in the US and more th
jeyben [28]

Answer:

(a) 0.119

(b) 0.1699

Solution:

As per the question:

Mean of the emission, \mu = 11.7 million ponds/day

Standard deviation, \sigma = 2.8 million ponds/day

Now,

(a) The probability for the water pollution to be at least 15 million pounds/day:

P(X\geq 15) = P(\frac{X - /mu}{\sigma} \geq \frac{15 - 11.7}{2.8})

P(X\geq 15) = P(Z \geq 1.178)

P(X\geq 15) = 1 - P(Z < 1.178)

Using the Z score table:

P(X\geq 15) = 1 - 0.881 = 0.119

The required probability is 0.119

(b) The probability when the water pollution is in between 6.2 and 9.3 million pounds/day:

P(6.2 < X < 9.3) = P(\frac{6.2 - 11.7}{2.8} < \frac{X - \mu}{\sigma} < \frac{9.3 - 11.7}{2.8})

P(6.2 < X < 9.3) = P(- 1.96 < Z < - 0.86)

P(6.2 < X < 9.3) = P(- 1.96 < Z < - 0.86)

P(Z < - 0.86) - P(Z < - 1.96)

Now, using teh Z score table:

0.1949 - 0.025 = 0.1699

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