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Fittoniya [83]
2 years ago
7

A class of 26 students bought a present for their principal. the present cost $111.80, tax included. how much did each student c

ontribute if the class shared the cost equally
Mathematics
1 answer:
makkiz [27]2 years ago
8 0
111.80 / 26 = 4.30.....so each student contributed $ 4.30
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Three times the 1st number plus the 2nd number plus twice the 3rd is 5. If three times the 2nd number is subtracted from the sum
Svetllana [295]

Answer:

c = 3,

b = 2

a = -1

Step-by-step explanation:

I want to start by saying let me know if there is anything you don't get.  I'd be happy to explain.

The best way to solve this, as with most math problems, is to write things out, or draw a picture if possible.  So let's call the first number a, second number band third c.  

Now let's write out what is described.

3a + b + 2c = 5

a + 3c - 3b = 2

2a + 3b - c = 1

So, since you are given three variables and three equations it indicates you should be able to find a pretty nice answer.  It's possible  things may not work out still, so keep that in mind.  Anyway, this is the method I liek to use with most systems of equations.

Taking the first equation, 3a + b + 2c = 5, we want to solve for one of the variables.  Since b doesn't have a coefficient let's do that.  So we want to subtract 3a and 2c from both sides to get b by itself.

3a + b + 2c = 5

b + 2c = 5 - 3a

b = 5 - 3a - 2c

Now we move on to the second equation.  a + 3c - 3b = 2, First we want to plug what we got or b in the last part in for b here.  so we got b = 5 - 3a - 2c so now a + 3c - 3b = 2 becomes a + 3c - 3(5 - 3a - 2c) = 2.  Let's simplify this real quick.

a + 3c - 3(5 - 3a - 2c) = 2

a + 3c - 15 + 9a + 6c = 2

-15 + 10a + 9c = 2

Now from here we want to get one of the variables by itself again.  This time let's do a.

-15 + 10a + 9c = 2

10a = 17 - 9c Now divide both sides by 10

a = 1.7 - .9c

We can also get our b = equation in terms of c as well, so I'll do that.

b = 5 - 3a - 2c

b = 5 - 3(1.7 - .9c) - 2c

b = 5 - 5.1 + 2.7c - 2c

b = -.1 + .7c

Now we tackle the third equation.  We want to plug in the b= term and a= term and then get c to just equal a number.  It might be confusing to explain so hopefully seeing the process will help.

2a + 3b - c = 1 Now use b = -.1 + .7c and a = 1.7 - .9c

2(1.7 - .9c) + 3(-.1 + .7c) - c = 1

3.4 - 1.8c - .3 + 2.1c - c = 1

3.1 - .7c = 1

-.7c = -2.1

c = 3

Now we work backwards and plug c into the b= term and the a= term.

b = -.1 + .7c now plug in c = 3

b = -.1 + .7(3)

b = -.1 + 2.1

b = 2

a = 1.7 - .9c Again plug in 3 for c

a = 1.7 - .9(3)

a = 1.7 - 2.7

a = -1

So c = 3, b = 2 and a = -1 should be the answer.  make sure to plug each of these into the starting three equations to check.  let me know if you didn't understand any of this, it was a looooooong explanation.  There is also a matrix method you could use, if you are familiar with matrices, and I'd be happy to explain that as well.  

5 0
3 years ago
Read 2 more answers
Justin has 34 quart of cranberry. if you divide the juice into glasses that hold 18 quart how many classes can justin fill?
Zina [86]
34/18 = 1.8.....so he can fill 1 glass full...with 16 qts left over
3 0
3 years ago
True or False: You can draw a quadrilateral with no parallel lines and at least one right angle.
Nat2105 [25]

Answer:

True.

Step-by-step explanation:

The answer is true. All you need is one 90 degree angle, two 50 degree angles, and one 170  degree angle. This creates a weird looking shape that is a quadrilateral with no parallel lines and at least one right angle.

Please mark me as brainliest. I need to rank up.

8 0
3 years ago
Help asap will mark BRAINLIEST
dsp73

x = 81 degrees (The sum of a triangle's angles must be 180 degrees. 48 + 51 = 99, and 180 - 99 = 81)

y = 99 degrees (Y and X are on a supplementary angle. Like a triangle, a supplementary angle's angles must add up to 180 degrees. 180 - 81 = 99)

z = 129 degrees (Z and the 51 degree angle are also on a vertical angle. 180 - 51 = 129)

Hope this helps!

4 0
2 years ago
Sort the property that characterizes either a trapezoid or a kite.
Pie

Trapezoid:

•Can have congruent diagonals. •Has one pair of opposite, parallel sides.

Kites:

•Has congruent adjacent sides.

•Has perpendicular diagonals.

5 0
3 years ago
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