Let the first angle be x and the second be y.
Supplementary angles add up to 180, so:
x + y = 180
Also, as given in the statement:
x = 4y - 25
Substituting into the first equation:
4y - 25 + y = 180
5y = 205
y = 41
x = 4(41) - 25
x = 139
One angle is 139° and the other is 41°.
multiply the 3 by how ever much to get 150
there will be 50 apples
Robbie bought the smallest amount. Let's use x for that amount.
Let's use n for amount that each following customer increases.
We have:
Robbie=x
Cameron=x+n
Louis=x+n+n
Tom=x+n+n+n
Charlie=x+n+n+n+n
We know that they bought total of 60 scones.
Robbie + Cameron + Louis + Tom + Charlie = 60
x + x+n + x+n+n + x+n+n+n + x+n+n+n+n = 60
5x + 10n = 60 /:5
x + 2n = 12
We are also given this information:
(Robbie + Cameron) = 3/7 * (Louis + Tom + Charlie)
We insert the equations from above:
(x + x+n) = 3/7 * (x+n+n + x+n+n+n + x+n+n+n+n)
2x + n = 3/7 * (3x + 9n) /*7
14x + 7n = 3* (3x + 9n)
14x +7n = 9x + 27n
We take everything on the left side.
14x + 7n - 9x - 27n = 0
5x - 20n = 0/:5
x - 4n = 0
Now we have two equations:
x + 2n = 12
x - 4n = 0
We solve second one for x and insert it into first one.
x + 2n = 12
x = 4n
4n + 2n =12
6n = 12 /:6
n = 2
x=4*2
x=8
Now we can solve for the amount for each customer.
Robbie=x = 8
Cameron=x+n = 8 + 2 = 10
Louis=x+n+n = 8 + 2 + 2 = 12
Tom=x+n+n+n = 8 + 2 + 2 + 2 = 14
Charlie=x+n+n+n+n = 8 + 2 + 2 + 2 + 2 = 16
First notice that the triangle with sides
and the triangle with sides
are similar. This is true because the angle between sides
in the smaller triangle is clearly
, while the angle between sides
in the larger triangle is clearly
. So the triangles are similar with sides
corresponding to
, respectively.
Now both triangles are
, which means there's a convenient ratio between its sides. If the length of the shortest leg is
, then the length of the longer leg is
and the hypotenuse has length
.
Since
is the shortest leg in the larger triangle, it follows that
, so
