Math Word Problem...?

Question

A piggy bank contains TWENTY coints with a total value of $2.80. The coins are NICKELS and QUARTERS. How many NICKELS are in the piggy bank?

Answer 1

hmmm. well we can start by figuring out how many quarters go into $2.80. the most quarters we could have is 11, so then with 11 quarters we would need one nickel to give us $2.80. With a total of 12 coins. So if we subtract a quarter we have to add 5 nickels. (since .25 equals 5x .05). By changing one quarter to 5 nickels we have 6 nickels and 10 quarters, giving us $2.80 and 16 coins. So we subtract one quarter and add 5 nickels again. Giving us 11 nickels and 9 quarters, with a total of $2.80 and 20 coins.

so 11 nickels

to see this mathmatically we would let x equal the number of nickels. then 20-x equal the number of quarters. and we know the total value is $2.80. so
.05x+.25(20-x)=2.80
.05x+5-.25x=2.80
-.20x= - 2.20
x= 11

so again 11 nickels is your answer

Answer 2

Let Q = the number of quarters, and N = the number of nickels:

(i) Q + N = 20 (There are 20 coins in the piggy bank in total)

Also, 0.25Q + 0.05N = 2.80

To make things easier, I'm going to turn all the decimal numbers above into whole numbers by multiplying both sides by 100:

(ii) 25Q + 5N = 280

From equation (i), we know that Q = 20 - N or that N = 20 - Q. I'm just going to choose (iii) Q = 20 - N to work with (since we want to know the number of nickels in the piggy bank). Now substitute (iii) into (ii) to get:

25(20 - N) + 5N = 280 => 500 - 25N + 5N = 280

Now collect like terms and simplify:

20N = 220 => N = 11

Therefore, there are 11 nickels in the piggy bank.

Answer 3

let n represent nickels and q represent quarters. There are 20 coins in all. Hence the first equation is n+q =20. For the other equation, I am sure how much is a nickel but I'm assuming that it is 1cent. So here is the second equation 0.01n + 0.25q = 2.80.
Here we have a pair of simultaneous eqations so we solve them.
n+q =20 eq.....1
0.01n + 0.25q = 2.80eq....2 *0.5
n + q = 20
0.025n + q = 1.4
Subtract both eq
0.975n = 18.6
n= 19.07 Hence there are 19 nickels
- = 18.6

Answer 4

11

Answer 5

let x represent the # of nickels
let y represent the # of quarters

then the equations are.....

x + y = 20

and

0.05x + 0.25y = 2.80


then, isolate y in the first equation ......

y=20 - x

then sub that into the second equation and solve for "x"

0.05x + 0.25(20 - x) = 2.80
0.05x + 5 - 0.25x = 2.80
0.05x - 0.25x = 2.80 - 5
-0.2x= -2.2
x= -2.2/-0.2
x=11

Therefore there are 11 nickels in the piggy bank and 9 quarters.

Answer 6

Let x = no. of nickels

$0.05x + $0.25(20 - x) = $2.80
$0.05x + $5.00 - $0.25x = $2.80
- $0.20x = $2.80 - $5.00
- $0.20x = - $2.20
x = - $2.20 / - $0.20
x = 11

Answer: There 11 nickels in the piggy bank.

Proof:
$0.05(11) + $0.25(20 - 11) = $2.80
$0.05(11) + $0.25(9) = $2.80
$0.55 + $2.25 = $2.80
$2.80 = $2.80

Answer 7

11 nickels


Two equations

n+q=20
&
.05n+.25q=$2.80

Solve for n in first equation
n=20-q

Replace n with 20-q in second equation
.05(20-q)+.25q=2.80

Now solve

1-.05q+.25q=2.80
1+.2q=2.80
.2q=1.80
q=9

20 coins in all
9 quarters


11 nickels

Answer 8

let q = number of quarters

Then $2.80 = $0.25*q+(20-q)*$0.05

2.80 = 0.25 q+ 1-0.05q = 0.2q+1
1.80 = 0.2q
q= 1.80/0.2 = 9
number of nickles = 20 -q = 11

Check
11 nickles = 0.55
9 quarters = 2.25
total =2.80

Answer 9

q = QUARTERS n =NICKELS

q+n =20
0.25q +0.05n =2.80
n= 11 q =9

Answer 10

n + q = 20
.05n + .25q = 2.80
figure it out girlfrien' you can do it!