A jar containing only nickels (n) and dimes (d) contains a total of 60 coins. The value of all the coins in the jar is $4.45. Write and solve a system of equations to find the amount of nickels and dimes that are in the jar.
Equation 1:
Equation 2:
The jar contains:
nickels and
dimes.
Blank 1:
Blank 2:
Blank 3:
Blank 4:

n + d = 60

0.05n + 0.1d = 4.45

The jar contains:  31 nickels and  29 dimes.

Step-by-step explanation:

Numbers of coins: n nickels and d dimes

Total number of coins: n + d

Total number of coins: 60

Equation 1: n + d = 60

Values of the coins:

n nickels are worth 0.05n

d dimes are worth 0.1d

Total value of all coins: 0.05n + 0.1d

Total value of coins: $4.45

Equation 2: 0.05n + 0.1d = 4.45

System of equations:

n + d = 60

0.05n + 0.1d = 4.45

Solve the first equation for n.

n = 60 - d

Substitute 60 - d for n in the second equation.

0.05n + 0.1d = 4.45

0.05(60 - d) + 0.1d = 4.45

3 - 0.05d + 0.1d = 4.45

3 + 0.05d = 4.45

0.05d = 1.45

d = 29

There are 29 dimes.

n + d = 60

n + 29 = 60

n = 31

There are 31 nickels.

The jar contains:

31 nickels and

29 dimes.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

7.3

step-by-step explanation: