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Andreyy89
3 years ago
8

Kevin and Randy Muise have a jar containing 70 coins, all of which are either quarters or nickels. The total value of the coins

in the jar is $7.50. How many of each type of coin do they have.​
Mathematics
1 answer:
Nikitich [7]3 years ago
6 0

Answer:

50 nickels, 20 quarters.

Step-by-step explanation:

System of equations (q = # of quarters, n = # of nickels):

<em>q + n = 70, 0.25q + 0.05n = 7.50</em>

the first equation can be changed to q = 70 - n, so we are able to <em>substitute q with 70 - n</em>.

So, it will look like <em>0.25*70 - 0.25n + 0.05n = 7.50</em>. This can be simplified to <em>0.2n = 10</em>, which means that n = 50.

Knowing that we can solve <em>q + 50 = 70</em>, which means that q = 20.

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ΔABC is a 45 - 45 - 90 triangle. The pattern of its sides is as follows:

Each leg = 1 unit (and both legs are that way, since the triangle is isosceles - so two sides are the same)

Hypotenuse = √2 units.

So if we know either leg, we multiply by √2 to get the hypotenuse. In reverse, we divide by √2 if we know the hypotenuse to get the measurement of a leg.

Our problem tells us that the hypotenuse AC is 10 units. We divide 10 by √2 to get the measurement of leg AB. Since it's a 45 -45 - 90 triangle, AB = BC.

AB = \frac{10}{\sqrt{2}}

= \frac{10\sqrt{2}}{\sqrt{2}\sqrt{2}} to rationalize the radical

= \frac{10\sqrt{2}}{2} = 5\sqrt{2}

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2 years ago
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Black_prince [1.1K]

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Step-by-step explanation:

Given :  The fuel efficiency of car = 7.6 km per kilogram

We also given that

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Then, \text{1 km}=\dfrac{1}{0.609}\text{ mile}

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\text{1 liter}=\dfrac{1}{3.785}\text{ gallon}

1 liter of gasoline = 0.729 kg

Then, \text{1 kg}=\dfrac{1}{0.729}\text{ liter}

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Now, the fuel efficiency of car will be :

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Hence,  the car’s fuel efficiency in miles per gallon= 4.5

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2 years ago
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Answer:

$27.59

Step-by-step explanation:

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Answer:

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Given:

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Therefore, the expression $32/x represents the price per pound.

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