The ratio of hens to rabbits in Mr. Potter's barn is 3 to 5. How many rabbits are in the barn if there are 27 hens?
2 answers:
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Answer:
7 and 13
Step-by-step explanation:
let the 2 numbers be x and y , x > y , then
x = y + 6 → (1)
(x + y) = y - 2 ( multiply both sides by 4 to clear the fraction )
x + y = 4y - 8 ( subtract 4y from both sides )
x - 3y = - 8 → (2)
Substitute x = y + 6 into (2)
y + 6 - 3y = - 8
- 2y + 6 = - 8 ( subtract 6 from both sides )
- 2y = - 14 ( divide both sides by - 2 )
y = 7
Substitute y = 7 into (1)
x = 7 + 6 = 13
The 2 numbers are 7 and 13
As shown in the figure, we have two straight line. One of them has a negative slope and the other has a positive one. In two dimensions, the equation for non-vertical lines is often given in the slope-intercept form by:
being m the slope of the line and <span>b the y-intercept of it.
On the other hand, if x = 0 then y = b.
First of all we will order the equations above without </span>inequalities<span> like this:
A. </span>
, 
<span>B. </span>, 
C.
,
D., 
<span>
As shown in the figure b = -1 for one straight and b = 4 for the second one. This values take place when x = 0. So, we discard C and D, because if x = 0, then:
</span>
For C, b = 1 and b = 4
For D, b = -1 and b = -4
Let's analyze A and B. So:
For A, m = 5 and m = 3
For B, m = 5 and m = -3
Therefore, we discard A because of the statement above.
Finally the answer is B. So, the inequalities are:
(1)
(2)
Let's prove this answer. We will take the point (2, 0) that is in the region in gray. So, substituting this point in the inequalities, we have:
(1)
(2)
In fact, this is true.
being m the slope of the line and <span>b the y-intercept of it.
On the other hand, if x = 0 then y = b.
First of all we will order the equations above without </span>inequalities<span> like this:
A. </span>
<span>B. </span>
C.
D.
As shown in the figure b = -1 for one straight and b = 4 for the second one. This values take place when x = 0. So, we discard C and D, because if x = 0, then:
</span>
For C, b = 1 and b = 4
For D, b = -1 and b = -4
Let's analyze A and B. So:
For A, m = 5 and m = 3
For B, m = 5 and m = -3
Therefore, we discard A because of the statement above.
Finally the answer is B. So, the inequalities are:
(1)
(2)
Let's prove this answer. We will take the point (2, 0) that is in the region in gray. So, substituting this point in the inequalities, we have:
(1)
(2)
In fact, this is true.