Question 72844: I feel like an idiot but here goes:
1 pony ride is $$2.00
2 " rides are $2.50
3 " " " $3.00
4 " " " $3.50
I need to write an expression using "n" to show the cost of "n" rides.
Its been 20 years since I did Algebra and I need to explain it to my 11 year old! Thank You!!
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The basic cost in this relationship is the $2.00 for the first ride. Each additional
ride adds 50 cents (or 0.5 dollars) to the previous cost.
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A relationship that would work is:
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C = (n - 1) times (0.50) plus $2.00
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where n represents the number of rides that you intend to buy. Also, n is limited to 1 or
more in value. And C represents the total cost for n rides.
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For example, if you intend to take 1 ride the equation becomes:
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C = (1-1)*(0.50) + $2.00 = 0 + $2.00 = $2.00
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but if you up the number of rides to 4, the equation becomes:
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C = (4-1)*(0.50) + $2.00 = (3)*(0.50) + $2.00 = $1.50 + $2.00 = $3.50
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If you have the time and desire to wander through the following explanation, then there
is another method.
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Namely you can do this problem graphically. Set up a coordinate system. Let the x-axis
(horizontal) have the values of n and let the y-axis (vertical) have the Cost values. Then
plot the points given to you by the problem ... namely (1, $2.00), (2, $2.50), (3, $3.00) and,
(4, $3.50). Now we need to analyze this graph, but first you have to remember that the
slope-intercept form for an equation such as this is:
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y = mx + b
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where m (the multiplier of the x value) is the slope of the graphed line, and b is the value
on the y-axis where the graph crosses.
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The slope is determined by putting your pencil on one of the known points. Then move the
point of your pencil horizontally 1 unit. Stop the point of your pencil. Then look
vertically and see how many units you have to move vertically upward to get back on the graph.
For example, put your pencil on the point (1, $2.00). Then move your pencil 1 unit horizontally
to the right. Stop the point of your pencil and your can see that you have to move upward
$0.50 to get back to the graph. So the slope, m, of the graph is $0.50 per unit. Put
this value in for m in the equation to get:
.
y = (0.50)x + b
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Now you need to find b, the point where the graph crosses the y-axis. Pick any one of
the given points and substitute its x and y values into the equation for y. Let' take
the point (2, $2.50). The 2 is the x value because it is measured on the x-axis. And the
$2.50 is the y value because it is measured on the y-axis. Substitute 2 for x and $2.50
for y to get:
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2.50 = (0.50)*2 + b
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Do the multiplication on the right side and find that:
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2.50 = 1.00 + b
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Subtract 1.00 from both sides to isolate b on the right side:
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1.50 = b
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Substitute this value for b back into our equation for y to get:
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y = (0.50)*x + 1.50
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Now all you need to do is to change y to C (the cost) because C is measured on the y-axis
and change x to n because n is measured on the x-axis. When you do this the equation
becomes:
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C = (0.50)*n + 1.50
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and this is another equation that will work. Let's check it. If we take 1 ride (that is n = 1),
then the cost becomes:
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C = (0.50)*1 + 1.50 = 0.50 + 1.50 = $2.00
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that works. Now assume you take 4 rides. The cost becomes:
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C = (0.50)*4 + 1.50 = 2.00 + 1.50 = $3.50
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that works also. Looks as if we have two good equations for the price of one.
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Hope that last method wasn't too complex. If your son has had graphing, it is a good refresher,
and if he hasn't this will be a good introduction to terms such as slope and intercept as
well as a chance to understand how to find points on the Cartesian coordinate system.
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Also hope that this helps you to recall math processes. Make good use of this site any time
you feel the need.
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Cheers!
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