Actually Welcome to the Concept of the linear equation in two variables.
So we have to form two equations to solve this.
Let the number of children be 'x' and number of adults be 'y'.
hence, we get as,
x+y = 630 ..... (1)
and also, to their total cost spending, we get as,
1.5x + 2.25y = 1170 ...... (2)
solving (1) and (2) we get as,
Number of children were = 330
and Number of Adults were = 300
(Solved in the attachment)
Answer:
( About ) 1,099 pounds
Step-by-step explanation:
The force required to keep this truck from rolling down the hill is opposed by the force of friction, comparative to the 2600 pounds of force against this friction. It should be that this opposing force is at work more towards the bottom of this hill, and thus the question asks the magnitude of latter force to keep this truck idle -
|| F || = sin( 25 ) * ( Fg ) = sin( 25 ) * ( 2600 lb ) = ( About ) 1098.80748 pounds
<u><em>This can be rounded to a solution of 1099 pounds</em></u>
Exponential word problems almost always work off the growth / decay formula, <span>A = Pert</span>, where "A" is the ending amount of whatever you're dealing with (money, bacteria growing in a petri dish, radioactive decay of an element highlighting your X-ray), "P" is the beginning amount of that same "whatever", "r" is the growth or decay rate, and "t<span>" is time. The above formula is related to the </span>compound-interest formula, and represents the case of the interest being compounded "continuously".
Note that the variables may change from one problem to another, or from one context to another, but that the structure of the equation is always the same. For instance, all of the following represent the same relationship:
<span>A<span> = </span><span>Pe<span>r<span>t </span></span></span></span>...or... <span>A<span> = </span><span>Pe<span>kt</span></span></span><span> ...or... </span><span>Q<span> = </span>Ne<span>kt</span></span><span> ...or... </span><span><span>Q<span> = </span>Q</span>0<span>e<span>kt</span></span></span>
<span>...and so on and so forth. No matter the particular letters used, the green variable stands for the ending amount, the blue variable stands for the beginning amount, the red variable stands for the growth or decay constant, and the purple variable stands for time. Get comfortable with this formula; you'll be seeing a lot of it.</span>
I hope this is useful !!!^_~!!!
To solve the system of equations, we first need to isolate one of the variables in one of the equations. For this example, I'll isolate x from the second equation, because it will be much easier and I'll end up with simpler fractions.
2x + y = -3 Given
2x = -y - 3 Subtract y from both sides
x = -1/2y - 3/2
Now, we need to substitute x in the other equation for -1/2y - 3/2 so that we can find y.
3(-1/2y - 3/2) - 7y = 4 Substitute
-3/2y - 9/2 - 7y = 4 Multiply
-17/2y - 9/2 = 4 Collect like terms (wow, this is turning out to be a tough one, isn't it?)
-17/2y = 17/2
y = -1
Wow, such complicated work for such a simple answer. Anyway, now we can plug that into our answer for x to get x's value.
<span>x = -1/2y - 3/2 Given
</span>x = -1/2(-1) - 3/2 Substitute
x = 1/2 - 3/2 Multiply
x = -1 Subtract
Therefore, the solution for the system of equations is (-1,-1). It can be a bit intimidating with all the fractions, but the question decided to be nice and give us simple answers.
Hope this helps!
