5 X 7 Photo Frames
Can somebody please help me with this algebra word problem? * Will choose best answer*?
At a photo shop, a 3 by 5 frame sells for $5.75, a 4 by 6 frame sells for $8.00, and a 5 by 7 grame sells for $10.75
A) Find a quadratic function of the form f(x)=ax^2 +bx+c that models the frame price in terms of the smaller dimension of the frame .
B) Using the model below, find the price of a 7 by 9 frame:
MODEL: (chart) x y
3 5.75
4 8.00
5 10.75
SHOW ALL STEPS.
WILL CHOOSE BEST ANSWER! thank you!
You need to solve this using a system of equations, the x values are the smaller dimensions of the frame so fill in the quadratic form
a(3)^2+3b+c=5.75 -> 9a+3b+c=5.75
a(4)^2+4b+c=8 -> 16a+4b+c=8
a(5)^2+5b+c=10.75 -> 25a+5b+c=10.75
That is the system of equations you need to solve by what ever method you prefer
so for example take the first equation and solve it for c leaving
c=5.75-9a-3b plug that in for c in the second equation leaving
16a+4b-9a-3b+5.75=8 combine terms to simplify
7a+b=2.25 rewrite for b
b=2.25-7a now just use the b and c values you found to fill in the third equation
25a+5b+c=10.75
25a+5(2.25-7a)+(5.75-9a-3(2.25-7a)=10.75 now everything is in terms of a so solve for a
25a+11.25-35a+5.75-9a-6.75+21a=10.75
2a=.5, a=.25 that is the value for a so back substitute it into you equation for b to find b
b=2.25-7a
b=2.25-7(.25) b=.5 now you have a and b so fill those into an equation to find c
9a+3b+c=5.75
9(.25)+3(.5)+c=5.75
2.25+1.5+c=5.75 c=2 you now have a, b and c so you can form your equation
.25x^2+.5x+2 or if you prefer fractions 1/4x^2 + 1/2x +2
finally to find the price for a 7 x 9 frame plug in 7 for x
.25(7)^2 +.5(7) +2 = price
12.25 +3.5 +2 = $17.75 for a 7 x 9 frame
if you have a graphing calculator you can also graph the function and see it passes through all the points in question
hope that helps
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