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Alisiya [41]
3 years ago
11

A box contains 81 coins, only dimes and nickels. The amount of money in the box is $5.30. How many dimes and how many nickels ar

e in the box?
The number of dimes is
The number of nickels is
Mathematics
1 answer:
Ksivusya [100]3 years ago
5 0

Answer:

  • 25 dimes
  • 56 nickels

Step-by-step explanation:

Let d represent the number of dimes. Then 81-d is the number of nickels and the total value in cents is ...

  10d +5(81-d) = 530

  5d +405 = 530 . . . eliminate parentheses

  d +81 = 106 . . . . . divide by 5

  d = 25 . . . . . . . . . subtract 81; number of dimes

  81 -d = 81 -25 = 56 . . . . . number of nickels

There are 25 dimes and 56 nickels in the box.

_____

<em>Comment on the method of solution</em>

It usually works well to let the variable represent the amount of the highest-value contributor (dimes). This keeps the numbers positive as the solution progresses.

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2 years ago
Solve for r.<br><br> r - 4.5 ≤ 11
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Step-by-step explanation:

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Evaluate each expression a3 for a=5
nadezda [96]
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4 0
3 years ago
rock is thrown upward with a velocity of 27 meters per second from the top of a 23 meter high cliff and it misses the cliff on t
ahrayia [7]

the rock will be at 11 meters from the ground level after 5.92 seconds

Step-by-step explanation:

The motion of the rock is a free-fall motion, since the rock is acted upon the force of gravity only. Therefore, it is a uniformly accelerated motion, so its position at time t is given by the equation:

y=h+ut+\frac{1}{2}at^2

where

h = 23 m is the initial height

u = 27 m/s is the initial velocity, upward

a=g=-9.8 m/s^2 is the acceleration of gravity, downward

t is the time

We want to find the time t at which the position of the rock is

y = 11 m

Substituting and re-arranging the equation, we find

11=23+27t-4.9t^2\\4.9t^2-27t-12=0

This is a second-order equation, which has solutions:

t=\frac{27\pm \sqrt{(-27)^2-4(4.9)(-12)}}{2(4.9)}=\frac{27\pm \sqrt{964.2}}{9.8}

So

t_1 = -0.41 s

t_2=5.92 s

The first solution is negative so we neglect it: therefore, the rock will be at 11 meters from the ground level after 5.92 seconds.

Learn more about free fall:

brainly.com/question/1748290

brainly.com/question/11042118

brainly.com/question/2455974

brainly.com/question/2607086

#LearnwithBrainly

8 0
3 years ago
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