Answer:
<u>There are 10 multiple-choice questions and 15 short-answer questions in the test</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Test worth 80 points
Multiple-choice questions are worth 2 points
Short-answer questions are worth 4 points
Multiple-choice questions + Short-answer questions = 25
2. How many multiple-choice questions are there?
Let's solve this problem, this way:
m = Multiple-choice questions
s = Short-answer questions
Our equations system is:
m + s = 25
2m + 4s = 80
Solving for m in the 1st equation:
m + s = 25
m = 25 - s
Substituting m in the 2nd equation and solving for s:
2m + 4s = 80
2 * ( 25 - s) + 4s = 80
50 - 2s + 4s = 80
2s = 80 - 50
2s = 30
<u>s = 30/2 = 15</u>
Substituting s in the 1st equation and solving for m:
m = 25 - 15
<u>m = 10 </u>
<u>There are 10 multiple-choice questions and 15 short-answer questions in the test</u>
-A rectangle<span> is a four-sided shape each angle is a </span>right angle<span>.
</span>
-A rhombus is a four-sided figure and all sides have equal length. Opposite sides are parallel and opposite angles are equal.
-A square has equal sides and every angle is a right angle. Opposite sides are parallel.
-A parallelogram<span> has opposite sides parallel and the sides lengths are the same. Opposite angles are equal </span>
I'll be honest, this is a pretty interesting question. I've never seen anything like it before!
We can start off by making equations with the given. If there are 100 heads, that means that the total number of chickens and pigs combined is 100. Thus, we can form our first equation:
p + c = 100
('p' represents number of pigs, and 'c' represents number of chickens)
We also know that there are 270 legs total. Since chickens have 2 and pigs have 4, we can make the following equation:
2c + 4p = 270
I suppose the quickest way to solve for this equation is to use the subtraction method. Put the equations on top of each other:
2c + 4p = 270
c + p = 100
___________
Multiply the bottom equation by -2;
2c + 4p = 270
-2c -2p = 100
____________
"Add" these two equations together:
2c + 4p = 270
-2c -2p = -200
___________
2p = 70
Divide both sides by 2:
p = 35
Ah, finally. Now that we know that there are 35 pigs, input this variable into the first equation to find the number of chickens:
c + 35 = 100
Subtract:
c = 65
There are 35 pigs and 65 chickens
-T.B.
