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Vesnalui [34]
3 years ago
9

Sierra has a total of 61 dimes and quarters in her piggybank. She has 3 more quarters than dimes. The coins have a total value $

10.90. How many dimes and how many quarters does she have? [hint: use the decimal values of the c coins to write an equation.]
Mathematics
1 answer:
cluponka [151]3 years ago
7 0
Since you have two unknowns, you must formulate 2 equations in order to solve the system. Let x be the numbers of dimes and y be the number of quarters. The equations are:

x + y = 61
y = x + 3

Since a dime is 1/10 of a dollar and a quarter is 1/4 of a dollar,
(1/10)x + (1/4)y = 10.90

We made 3 equations. The system is overspecified. Let's just use the first two equations and apply it to the third for verification.

x + (x + 3) = 61
Solving for x,
x = 29
y = 29 + 3 = 32

Verifying,
(1/10)(29) + (1/4)(32) = 10.90

Hence, there are 29 dimes and 32 quarters.
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Answer:

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Step-by-step explanation:

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On reflection on y=x line the new points we get for line LM are

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Slope of line LM

m=\frac{y_2-y_1}{x2-x1}\\m=\frac{(-9)-(-4)}{1-9} \\m=\frac{-9+4}{-8}=\frac{-5}{-8}\\m=\frac{5}{8}

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m_{JK} =\frac{5}{8} , m_{LM}=\frac{5}{8}

Since slopes of lines JK and LM are same therefore we can say that these are parallel to each other.

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