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OlgaM077 [116]
3 years ago
15

Mr.marichal has quarters ,dimes,and pennies in a jar.he has twice as many quarters as oennies.he also has 5 more dimes than penn

ies.the total value of the coins is $6.60.how many of each type of coin does he have
Mathematics
1 answer:
liberstina [14]3 years ago
5 0

He has 20 quarters, 15 dimes and 10 pennies.

Step-by-step explanation:

Let,

Quarters = x

Dimes = y

Pennies = z

We know that,

A quarter is 25 cents, dime is 10 cents and penny is 1 cent.

Total amount = $6.60 = 6.60*100 = 660 cents

According to given statement;

25x+10y+z=660   Eqn 1

x=2z    Eqn 2

y=z+5   Eqn 3

Putting these values of x and y in Eqn 1

25(2z)+10(z+5)+z=660\\50z+10z+50+z=660\\61z=660-50\\61z=610\\

Dividing both sides by 61;

\frac{61z}{61}=\frac{610}{61}\\z=10

Putting z=10 in Eqn 2

x=2(10)\\x=20

Putting z=10 in Eqn 3

y=10+5\\y=15

He has 20 quarters, 15 dimes and 10 pennies.

Keywords: linear equations, substitution method

Learn more about linear equations at:

  • brainly.com/question/10978575
  • brainly.com/question/11025333

#LearnwithBrainly

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There is a triangle with a perimeter of 63 cm, one side of which is 21 cm. Also, one of the medians is perpendicular to one of t
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Answer:

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Step-by-step explanation:

There is no info in the problem/s  text which one of the triangle's  side is 21 cm. That is why we have to try all possible variants.

Let the triangle is ABC . Let the AK is the angle A bisector and BM is median.

Let O is AK and BM cross point.

Have a look to triangle ABM.  AO is the bisector and AOB=AOM=90 degrees (means that AO is as bisector as altitude)

=> triangle ABM is isosceles => AB=AM  (1)

1. Let AC=21   So AM=21/2=10.5 cm

So AB=10.5 cm as well.  So BC= P-AB-AC=63-21-10.5=31.5 cm

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2. Let AB=21 So AM=21 and AC=42 .So  BC= P-AB-AC=63-21-42=0 cm- such triangle doesn't exist.

3. Finally let BC=21 cm. So AB+AC= 63-21=42 cm

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Let check if this triangle exists ( if the triangle's inequality fulfills).

BC+AB>AC    21+14>28 - correct=> the triangle with the sides' length 21cm,14 cm, 28cm exists.

This variant is the only possible solution of the given problem.

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