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matrenka [14]
3 years ago
6

Lizzie has 30 coins that total $4.80. All of her coins are dimes, D, and quarters, Q. Algebraically determine how many of each t

ype of coin did Lizzie have?
Mathematics
1 answer:
Gnom [1K]3 years ago
6 0

Lizzie has 18 dimes and 12 quarters

<em><u>Solution:</u></em>

Let "d" be the number of dimes

Let "q" be the number of quarters

We know that,

value of 1 dime = $ 0.10

value of 1 quarter = $ 0.25

Given that LIzzie has 30 coins

number of dimes + number of quarters = 30

d + q = 30 ---- eqn 1

Also given that the coins total $ 4.80

number of dimes x  value of 1 dime + number of quarters x  value of 1 quarter = 4.80

d \times 0.10 + q \times 0.25 = 4.80

0.1d + 0.25q = 4.8 ------ eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

d = 30 - q ---- eqn 3

Substitute eqn 3 in eqn 2

0.1(30 - q) + 0.25q = 4.8

3 - 0.1q + 0.25q = 4.8

0.15q = 1.8

<h3>q = 12</h3>

From eqn 3,

d = 30 - 12

<h3>d = 18</h3>

Thus she has 18 dimes and 12 quarters

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angelo's mother put $50 on a lunch card he spends the same amount each day for lunch. what is the constant rate of change for th
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Given that Angelo spends the same amount everyday from the amount in

the lunch card, the function of the amount remaining is a linear function.

  • The constant rate of change of the function is; <u>-5.25</u>
  • The two ordered pair used to find the constant rate of change are; <u>(1, 44.75) and (2, 39.5)</u>

Reasons:

The amount Angelo's mother put on the lunch card = $50

A possible table of values to the question is presented as follows;

\begin{tabular}{r|c|c|c|c|}Days&0&1&2&3\\Money Remaining&&44.75&39.5&\end{array}\right]

Required:

The constant rate of the function that gives the amount remaining from the

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Solution:

  • Slope \ or \ constant \ rate \ of \ change  = \mathbf{\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}

The two ordered pair that can be used to find the slope or constant rate of change are;

(x₁, y₁) = (1, 44.75), and (x₂, y₂) = (2, 39.5)

With the above two ordered pairs, we have the constant rate of change of the function given as follows;

Constant \ rate \ of \ change\  (The \ slope) =\dfrac{39.5-44.75}{2-1} = \mathbf{ -5.25}

The constant rate of change for the function that gives the amount remaining in the lunch card is; <u>-5.25</u>

Learn more about the constant rate of change of a function here:

brainly.com/question/10007759

brainly.com/question/16644839

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Step-by-step explanation:

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