Hello from MrBillDoesMath!
Answer:
n = 5
Discussion:
Let the original number be "n" Translating the problem statement to mathematical symbolism:
n + 4 = 19 - 2n => add 2n to both sides
n + 2n + 4 = 19 - 2n + 2n => combine like terms
3n + 4 = 19 => subtract 4 from both sides
3n = 19 -4 = 15 => divide both sides by 3
n = 15/3 =5
Check: Does 5 +4 = 19 - 2(5)? Does 9 = 9? Yes. so the value for n is confirmed correct.
Thank you,
MrB
To understand the problem, let's first draw a free body diagram of the forces exerted by Judy and Ike on the truck. (Refer to the left side of the attachment).
To solve for the resultant, we just use the tip-to-tail method. This is illustrated on the right side of the attachment.
We can see that the tip-to-tail method forms a right triangle thus we can just apply the Pythagorean theorem in solving for Ike's force.



ANSWER: Ike must pull the truck with a force of 16.0 N.
The tangent of the angle is
... tan(α) = ay/ax = -8.6/6.1
Then the angle (measured CCW from +x) is
... α = arctan(-86/61) ≈ 305°
A.) 10x + 7.5 (0) =420
10x = 420
420 / 10 = 42
x = 42 > ( 42,0 )
10(0) + 7.5y = 420
7.5y = 420
420 / 7.25 = 56
y = 56 > ( 0,56 )
(42,0) (0,56)
B.) The x intercept means that there was 42 ,minutes spent biking. The y intercept means that there was 56 minutes spent in line skating.
C.) (21 ,28) - (14,37) - (28,18)