SOLUTION: write an equation in standard form for the given information (9,4),m=-1/3 (-3,-1) (2,-2) A piggy bank contains only quarters and dimes. The total value in the bank is $5.50.

Algebra ->  Testmodule -> SOLUTION: write an equation in standard form for the given information (9,4),m=-1/3 (-3,-1) (2,-2) A piggy bank contains only quarters and dimes. The total value in the bank is $5.50.       Log On


   

Question 117593: write an equation in standard form for the given information
(9,4),m=-1/3
(-3,-1) (2,-2)
A piggy bank contains only quarters and dimes. The total value in the bank is $5.50.
write an equation in stnadard form that models the possible combinations of nickels and quarters in the piggy bank.
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
q = number of quarters
d = number of dimes
25q+%2B+10d+=+550

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
write an equation in standard form for the given information
(9,4),m=-1/3
In the slope/intercept form y = mx + b:
y = -1%2F3x + b
Substitute for x & y and find b
4 = -1%2F3(9) + b
4 = -3 + b
4 + 3 = b
b = 7
Therefore we have the slope intercept equation:
y = 1%2F3x + 7
Get rid of the fraction multiply by 3
3y = -x + 21
Arrange in the standard form, add x to both sides
x + 3y = +21; check equation by substituting the given values for x and y
:
:
:
(-3,-1) (2,-2)
Find the slope using the slope equation: m = %28%28y2-y1%29%29%2F%28%28x2-x1%29%29
x1 = -3; y1 = -1; x2 = 2; y2 = -2; substitute in the slope equation:
m = %28%28-2-%28-1%29%29%29%2F%28%282-%28-3%29%29%29 = %28%28-2%2B1%29%29%2F%28%282%2B3%29%29 = -1%2F5
:
Use the slope/intercept equation again
y = -1%2F5x + b
:
Substitute x1 and y1 and find b
-1 = -1%2F5%29(-3) + b
-1 = 3%2F5 + b
-5%2F5 - 3%2F5 = b
-8%2F5 = b
Therefore we have the point/slope equation (y = mx + b) of:
y = -1%2F5x - 8%2F5
Multiply by 5 to get rid of the denominator
5y = -x - 8
Convert to standard form
x + 5y = -8; You can check it by substituting the given values for x and y
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A piggy bank contains only quarters and dimes. The total value in the bank is $5.50.
write an equation in standard form that models the possible combinations of nickels and quarters in the piggy bank.
:
Let x = no of dimes; Let y = no. of quarters.
.05x + .25y = 5.50
:
They don't like fractions or decimals in the standard form, mult eq by 100
5x + 25y = 550
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