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Lucinda has a pocketful of dimes and quarters with a value of $6.20. The number of dimes is 18 more than 3 times the number of quarters. How many dimes and how many quarters does Lucinda have?

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calculista

Answer:

The number of dimes is 42 and the number of quarters is 8

Step-by-step explanation:

Let

x -----> the number of dimes

y -----> the number of quarters

Remember that

1 dime=$0.10

1 quarter=$0.25

we know that

0.10x+0.25y=6.20 -----> equation A

x=3y+18 ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (42,8)

see the attached figure

therefore

The number of dimes is 42 and the number of quarters is 8

Ver imagen calculista
ardni313

There are 42 dimes and 8 quarters

Further explanation

The two-variable linear equation is a linear equation that has 2 variables and the exponent is one

Can be stated in the form:

[tex] \large {\boxed {\bold {ax + bx = c}}} [/tex]

x, y = variable

In this equation system there are coefficients and variables whose solutions can use:

  • 1. substitution
  • 2. elimination
  • 3. graph
  • 4. mix

We can state the problem in the form of algebraic equations

  • Lucinda has a pocketful of dimes and quarters with a value of $ 6.20

we translate this sentence into Algebraic expressions:

dime = D = $ 0.10

quarter = Q = $ 0.25

Then the equation becomes:

0.1D + 0.25Q = 6.20

  • The number of dimes is 18 more than 3 times the number of quarters

we translate this sentence into Algebraic expressions:

D = 18 + Q

D - 3Q = 18

We solve the two equations with substitution and elimination

1. elimination

0.1D + 0.25Q = 6.20 x 10

D - 3Q = 18                 x 1

------------------------------------

D + 2Q = 62

D - 3Q = 18

----------------------------------- -

5.5Q = 44

Q = 8

2. substitution

D - 3Q = 18

D - 3.8 = 18

D - 24 = 18

D = 42

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