1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
melisa1 [442]
3 years ago
12

joe has a piggy bank with $8.90 split upon nickels, dimes, and quarters. The piggy bank contains 76 coins in all. The number of

dimes is equal to the sum of quarters and nickels. How many of each coin does he have ?
Mathematics
1 answer:
kozerog [31]3 years ago
4 0

Answer:

There are 38 dimes, 22 nickels and 16 quarters.

Step-by-step explanation:

Let n, d and q represent the # of nickels, dimes and quarters respectively.

Then n + d + q = 76

The value of a nickel is $0.05; that of a dime is $0.10, and that of a quarter is $0.25.

Thus, the value of n nickels is $0.05n (and so on).

The total value of the coins is $0.05n + $0.10d + $0.25q = $8.90.

d = n + q allows us to eliminate d.

First, n + d + q = 76 becomes n + (n + q) + q = 76, and second:

$0.05n + $0.10(n + q) + $0.25q = $8.90.  Here we have succeeded in eliminating d from two different equations, and now we have these two different equations in two unknowns (n and q), which is solvable.

Simplifying both equations, we get:

2n + 2q = 76 and

5n + 10n + 10q + 25q = 890, or 15n + 35q = 890

Let's use the substitution method of solving linear equations:

Rewrite 2n  + 2q = 76 as n + q = 38, or n = 38 - q.  Substituting this result into the second equation, we get:

15(38 - q) + 35 q = 890, or

  570 - 15q + 35q = 890, or

   570 + 20 q = 890.  Then 20q = 890 - 570 = 320, and q = 320/20 = 16.

There are 16 quarters.  Thus, the number of nickels is n = 38 - 16 = 22.

Finally, since n + d + q = 76, 22 + d + 16 = 76, or:

22 + d = 60, or d = 60 - 22 = 38.

There are 38 dimes, 22 nickels and 16 quarters.

You might be interested in
Solve the system of equations.<br><br> 5x + y = 9<br> 3x + 2y = 4
tiny-mole [99]
Y=-5x+9

3x+2(-5x+9)=4
3x-10x+18=4
-7x=4-18
-7x=-14
x=2

5(2)+y=9
10+y=9
y=9-10
y=-1

The answer is (2,-1) :)
5 0
3 years ago
Read 2 more answers
-1 - 5 (-2k+3)= -76​
disa [49]

Answer:

k= -6

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

7 0
3 years ago
Read 2 more answers
Naomi‘s fish is 40 mm long. Her guinea pig is 25 cm long. How much longer is your guinea pig than her fish?
hjlf

Answer:

21 cm

Step-by-step explanation:

25-4=21

3 0
3 years ago
Urgent help please . it’s important and i’m stuck
Nina [5.8K]

Answer: The image wont lode, sorry.

Step-by-step explanation:

5 0
2 years ago
2.5 kg of potatoes is £1.40<br> What is the cost of 4.25
Kobotan [32]
2.18


Mark brainliest please


Hope this helps
5 0
2 years ago
Other questions:
  • In the rhombus,8y-6 . Find the value of y.
    9·1 answer
  • The interior angle of a triangle measues 75, (5w+25), And (2w+10)
    11·2 answers
  • Which represents the number 16,807 in exponential form
    6·1 answer
  • A packet of crisps contains 50g. If a “new size” packets contain 15% more, how many grams of crisps are in the “new size” packet
    11·1 answer
  • The area of the patio is 216 square feet. Write an equation that represents the area of the patio
    13·1 answer
  • The rain that occurs after a volcano erupts would most likely be
    10·2 answers
  • Find f(-3) when f(x) = -x²+1​
    11·1 answer
  • 75 - { ( 8 x 3 ) + 6 }
    6·2 answers
  • What is another way to write the expression: t. {14-5} plz I need help on this FAST
    5·1 answer
  • I need Help!!!<br><br><br>(Question is attached)
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!