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Masja [62]
3 years ago
12

A woman has 21 total coins in her pocket, all of which are either dimes or quarters. If the total value of her change is $3.90,

how many dimes and how many quarters does she have? Write the number of dimes, then the number of quarters separated by a comma.
Mathematics
2 answers:
Elza [17]3 years ago
8 0

Answer with Step-by-step explanation:

Let there be d dimes and q quarters

A woman has 21 total coins in her pocket.

⇒ d+q=21    ------(1)

1 dime=$ 0.1

1 quarter=$ 0.25

The total value of her change is $3.90

⇒ 0.1d+0.25q=3.90

Multiplying both sides by 100,we get

10d+25q=390     --------(2)

(2)-10×(1)

10d+25q-10d-10q=390-210

15q=180

Dividing both sides by 15, we get

q=12

Putting value of q in (1),we get

d=9

Hence, Number of dimes=9

and number of quarters=12

Write the number of dimes, then the number of quarters separated by a comma.

9,12

Alisiya [41]3 years ago
6 0

Answer:

<h2>The woman has 12 quarters and 9 dimes.</h2>

Step-by-step explanation:

Givens

  • The woman have 21 total coins.
  • The coins are distributed between dimes ad quarters.
  • The total value of her change is $3.90.

With this information we can construct a system of equations, where d is dimes and q is quarters.

d+q=21, because there are 21 coins between dimes and quarters.

Now, we know that one dime values 10 cents, and one quarter values 25 cents.

0.10d+0.25q=3.90, because the woman has $3.90 in total.

Then, we isolate d in the first expression

d=21-q

And we substitute it in the second expression

0.10d+0.25q=3.90\\0.10(21-q)+0.25q=3.90\\2.1-0.10q+0.25q=3.90\\0.15q=3.90-2.1\\q=\frac{1.80}{0.15} \\q=12

Then, we use this value to find the other one

d=21-q\\d=21-12\\d=9

Therefore, the woman has 12 quarters and 9 dimes.

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Quincy was stuck inside during an afternoon rainstorm. He spent 20 minutes reading books, 18 minutes eating lunch, 12 minutes wa
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Answer:

The answer is B. He spent 3 minutes eating lunch for every 10 minutes.

Step-by-step explanation:

He spent stuck inside during the brainstorm for:

20+18+12+10= 60 minutes in total.

And now we want to know what he did for every 10 minutes he spent in the rainstorm. To do that we need to divide what he did for every 10 minutes by the total of minutes that he was stuck:

\frac{10}{60} =\frac{1}{6}

And now we can multiply the time of the activities by 1/6 to get the time he did each activity every 10 minutes.

Reading:

20*\frac{1}{6} = 3.33 minutes reading for every 10 minutes.

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Therefore he spent 3 minutes eating lunch for every 10 minutes.

4 0
3 years ago
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If you wanted to find the lengths, you would add both widths together (same as multiplying a width by two) and add that to the two lengths equaled to the perimeter.

So, 22 * 2 + 2x = perimeter of rectangle. We added all four sides together.

We know that the perimeter is at least 165, so 22 * 2 + 2x = 165. Here's the twist. They want the most minimum possible length. So, what answer choice gives you 165 or less for the most minimum or smallest length while still getting to 165?
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Answer:

Step-by-step explanation:

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