Answers:
- Total equation: x+y = 80
- Legs equation: 2x+4y = 248
- How many ducks? 36
- How many cows? 44
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Further explanation:
- x = number of ducks
- y = number of cows
x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.
That equation can be solved to y = 80-x after subtracting x from both sides.
The legs equation is 2x+4y = 248 because...
- 2x = number of legs from all the ducks only
- 4y = number of legs from all the cows only
- 2x+4y = total number of legs from both types of animals combined
We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248
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Let's plug y = 80-x into the second equation and solve for x.
2x+4y = 248
2x+4( y ) = 248
2x+4( 80-x ) = 248
2x+320-4x = 248
-2x+320 = 248
-2x = 248-320
-2x = -72
x = -72/(-2)
x = 36
There are 36 ducks
Now use this x value to find y
y = 80-x
y = 80-36
y = 44
There are 44 cows.
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Check:
36 ducks + 44 cows = 80 animals total
36*2 + 44*4 = 72 + 176 = 248 legs total
The answers are confirmed.
Answer:
The approximate circumference is 62.8 mm
Step-by-step explanation:
Circumference is basically the perimeter of the circle
Circumference is given by
Here the diameter is 20 mm, so the radius will be half of diameter = 10 mm
Substituting the given values, in above equation, we get -
Circumference =
mm
The approximate circumference is 62.8 mm
Answer:
Angelina should buy 9 packs of pens and 8 packs of pencils.
Step-by-step explanation:
Each pack of pens = 8 pens
Each pack of pencils = 9 pencils.
Also we know that, Commutative Property of Multiplication states that
a x b = b x a for any two numbers a and b.
So, 8 x 9 = 72 = 9 x 8
Hence, she should buy 9 packs of pens, so she will have 9 x 8 = 72 pens.
And she should buy 8 packs of pencils, she will have 8 x 9 = 72 pencils.
The answer is 94 because if you add 8 more it would be 102. 14 + (8x10)
