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qwelly [4]
3 years ago
6

Solve the following: Three times the 1st number plus the 2nd number plus twice the 3rd is 5. If three times the 2nd number is su

btracted from the sum of the 1st and three times the 3rd number, the result is 2. If the 3rd number is subtracted from two times the 1st number and three times the 2nd, giving a result of 1. Find the three numbers.
Mathematics
1 answer:
Karolina [17]3 years ago
3 0
Three times the 1st number plus the 2nd number plus twice the 3rd is 5 is the same as 3x+y+2z=5. If three times the 2nd number is subtracted from the sum of the 1st and three times the 3rd number, the result is 2 is just x+3z-3y=2. And if the 3rd number is subtracted from two times the 1st number and three times the 2nd, giving a result of 1 means 2x+3y-z=1. Then you use substition on these equations to get a equation where one variable equals 2 others, like using the first to get y=5-2z-3x and then this can be substituted into the other two to get x+3z-3(5-2z-3x)=2 and 2x+3(5-2z-3x)-z=1 we can then simplify and subtract the equations. After simplification we have 10x+9z=17 and 7z+7x=16 which can be turned into 70x+63z=119 and 70x+70z=160 which can be then subtracted to get that 7z=41 and z=41/7. Now we backtrack to a two variable equation like 7z+7x=16 and plug in to find x. So after plugging in we get 41+7x=16 and 7x=-25 so x=-25/7. Now we choose a 3 variable equation and plug in. So taking y=5-2z-3x we plug in 41/7 for z and -25/7 for x to get y=5-82/7+75/7 and y=5-7/7 and y=4. Therefore x = -25/7 y = 4 and z = 41/7.
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5th grade math. Correct answer will be marked brainliest.
Masteriza [31]

Answer:

Part A: 100x=235

B: 2.35

C: The weight of the fish would differ by 211.5 because if you find the difference between the equation's answers, 235 and 23.5, it's 211.5

Step-by-step explanation:

5 0
3 years ago
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You mix soda water, fruit punch concentrate, and ginger ale in the ratio of 1 : 2 : 5 to make fruit punch. How many pints of eac
SIZIF [17.4K]
All you do is 1x+2x+5x=8x then you turn 4 s into pints. 1 gallon equals 4 pints 4*4=16 pints. 8x=16 x=2. Then you multiply everything by 2

1*2=2 
2*2=4
2*5=10

2pints of soda water
4 pints of fruit punch
10 pints of ginger ale
3 0
3 years ago
What is the answer to this equation 6x+3-6x=3
aev [14]

Answer:

0=0

Step-by-step explanation:

6x-6x=0

cancel the terms on both sides of the equation

0=0  the sum of two opposites equals zero

this statement is correct

5 0
3 years ago
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
Neporo4naja [7]


Every body has two hands so we have to multiply 66 by 2.

66 multiplied by 2 is equal to 132

The answer is 132.

hope it helps.

Can you choose mine as the brainliest answer <u><em>please please?</em></u>

4 0
3 years ago
Read 2 more answers
A manufacturing plant earned $80 per man-hour of labor when it opened. Each year, the plant earns an additional 5% per man-hour.
baherus [9]

A function that gives the amount that the plant earns per man-hour t years after it opens is \mathrm{A}(\mathrm{t})=80 \times 1.05^{\mathrm{t}}

<h3><u>Solution:</u></h3>

Given that  

A manufacturing plant earned $80 per man-hour of labor when it opened.

Each year, the plant earns an additional 5% per man-hour.

Need to write a function that gives the amount A(t) that the plant earns per man-hour t years after it opens.  

Amount earned by plant when it is opened = $80 per man-hour

As it is given that each year, the plants earns an additional of 5% per man hour

So Amount earned by plant after one year = $80 + 5% of $80 = 80 ( 1 + 0.05) = (80 x 1.05)

Amount earned by plant after two years is given as:

=(80 \times 1.05)+5 \% \text { of }(80 \times 1.05)=(80 \times 1.05)(1.05)=80 \times 1.052

Similarly Amount earned by plant after three years =80 \times 1.05^{t}

\begin{array}{l}{\Rightarrow \text { Amount earned by plant after } t \text { years }=80 \times 1.05^{t}} \\\\ {\Rightarrow \text { Required function } \mathrm{A}(t)=80 \times 1.05^{t}}\end{array}

Hence a function that gives the amount that the plant earns per man-hour t years after it opens is \mathrm{A}(t)=80 \times 1.05^{t}

5 0
3 years ago
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