Kira sent 19 text messages, Goran sent 14 text messages and Joe sent 57 text messages.
Let be "k" the number of text messages that Kira sent during the weekend, "g" the number of text messages that Gora sent during the weekend and "j" the number of text messages that Joe sent during the weekend.
We know know that they sent a total of 90 text messages then:
Goran sent 5 fewer messages than Kira. This is:
And Joe sent 3 times as many messages as Kira. Then:
The steps to solve this are:
- Substitute the second equation and the third equatio into the first equation and then solve for "k":
- Substitute this value into the second equation to find "g":
- Substitute the value of "k" into the third equation to find "j":
a = a1
first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.
pythagorean theorem formula:
a^2 + b^2 = c^2
(x - 20)^2 + (x - 40)^2 = x^2
x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2
x^2 -120x + 2000 = 0
(x - 100)(x - 20) = 0
x - 100 = 0 or x - 20 = 0
x = 100 or x = 20
we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.
perimeter = sum of the lengths of the sides
perimeter = x + x - 20 + x - 40
perimeter = 3x - 60
replace x with 100.
perimeter = 3(100) - 60
perimeter = 300 - 60
perimeter = 240