Monica’s school band held a car wash to raise money for a trip to a parade in New York City. After washing 125 cars, they made $775 from a combination of $5.00 quick washes and $8.00 premium washes.Let x represent the number of quick washes and let y represent the number of premium washes. Which system of linear equations represents the situation?
5x + 8y = 775 and x + y =125
5x – 8y = 125 and x + y = 775
5x + 8y = 775 and x – y = 125
5x – 8y = 125 and x – y = 775

Answers

Answer 1

Answer:

Let x represent the number of quick washes and let y represent the number of premium washes.

1. One quick wash costs $5, then x quick washes cost $5x.

One premium wash cost $8, then y premium washes cost $8y.

They made $775 from a combination of quick and premium washes, then in total they made $(5x+8y) that is $775. The first equation is

5x+8y=775.

2. They had washed 125 cars, x cars by quick wash and y cars by premium wash, that is x+y in total. Then tha second equation is

x+y=125.

Only option A represents the situation.

Answer 2

Answer: Given:
quick washes = x ; $5
premium washes = y ; $8

x + y = 125
5x + 8y = 775

Correct answer is the 1st option.

x = 125 - y
5(125 - y) + 8y = 775
625 - 5y + 8y = 775
3y = 775 - 625
3y = 150
y = 150/3
y = 50 number of premium washes

x = 125 - 50
x = 75 number of quick washes

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Pretty please help guys!!

Answers

For #1:

y = x + 4

Parallel lines have the SAME slope, this equation is in the form of y = mx + b, where 'm' is the slope. So the slope here is 1.

To find the equation of a line that passes through (2, 2) and has a slope of 1, we can plug it into point-slope form:

y - y1 = m(x - x1)

Where 'y1' is the y-value of the point, 'x1' is the x-value of the point, and 'm' is the slope.

y - 2 = 1(x - 2)

Distribute 1 into the parenthesis:

y - 2 = x - 2

Add 2 to both sides:

y = x

So your equation is y = x.

IGreen's answer is elegant and totally correct, but I'm guessing that you'll get
confused when you try to dig through it. Allow me to present a simpler method,
if I may:

-- In your picture, we can only see 1, 3, and 5. We can't see enough of 2, 4,
or 6 to work on them.
But ALL six of the problems on this page are examples of the same thing:
Write the equation of a line when you know the slope and one point on the
line. That's it !

Rules to use:

-- The slope-intercept form of the equation of a line is

   y = (slope) x + (intercept)

-- When two lines are parallel, they have the SAME slope.

-- When two lines are perpendicular, their slopes are negative reciprocals.
. . . . . 'negative' means the opposite sign
. . . . . 'reciprocal' means flip a fraction over, or take 1 / (a whole number).
negative reciprocal of 3/4 is (- 4/3)
negative reciprocal of -2 is (+ 1/2)
etc.

And now you're ready to solve all six problems.

#1). through (2,2) and parallel to [ y = x + 4 ] .

"parallel" means the new line has the same slope as [ y = x + 4 ] .
What is the slope of [ y = x + 4 ] ? It's the '1' that's not written next to 'x'.
So the new line is going to be [ y = 1x + b ].
All you need to find is 'b'.

Whatever equation you find for the new line, it'll be true for every point on
the line.
You already know one point on the new line ... (2,2) ... The equation must be
true for this point. Write this point into the new equation:

   y = 1x + b

   2 = 1(2) + b

   2 = 2 + b

What is 'b' ? Subtract 2 from each side, and you have

   0 = b .

So the equation of the new line is [ y = x + 0 ] or just [ y = x ].

That's how to do them when the new line is parallel to a given line.
Now do one where the new line is perpendicular to a given line.

#5). through (1, -5) and perpendicular to [ y = -1/8 x + 2 ].

What's the slope of the new line ? In order to be perpendicular to this one,
the slope of the new one must be the negative reciprocal of -1/8 .
The negative of -(anything) is +.
The reciprocal of 1/8 is 8 .
So the slope of the new line is +8 .
The equation of the new line is . . . [ y = 8x + b ].
How to find 'b' ?
Take the point you know on the new line (1, -5), and write it into this equation:

   -5 = 8(1) + b

Squeeze 'b' out of this, and you have the equation of your new line.

All of the other problems on the page are just like these. All together,
on the whole page, there are 4 problems where the new line is parallel
to the given line, and two problems where the new line is perpendicular
to the given one. You should be able to whip out all six in about 15 minutes.

Good luck.

Rewrite this expression using the distributive property then simplify.
2/3(6x+12)