Question

a piggy bank contains nickels and dimes. there are 160 total coins valuing 10.50. think about a system of equations that can be used to represent the number of nickels and dimes, and then through using substitution to solve the system of equations. how many nickels are in the piggy bank?

Answer 1

Answer: There are 110 nickels in the piggy bank.

Step-by-step explanation:

Let the number of nickels be 'n'.

Let the number of dimes be 'd'.

Total amount = 10.50

Total number of coins = 160

So, According to question, it becomes,

$n+d=160\\\\d=160-n\\\\0.05n+0.1d=10.50\\\\0.05n+0.1(160-n)=10.50\\\\0.05n+16-0.1n=10.50\\\\-0.05n=10.50-16=-5.5\\\\n=\dfrac{5.5}{0.05}=110$

Hence, there are 110 nickels in the piggy bank.

Answer 2

Ok here's your system:

n+d=160
0.05n+0.10d=10.50

Steps:

I will try to solve your system of equations.

d+n=160;0.1d+0.05n=10.5

Step: Solved+n=160for d:

d+n+−n=160+−n(Add -n to both sides)

d=−n+160

Step: Substitute−n+160fordin0.1d+0.05n=10.5:

0.1d+0.05n=10.5

0.1(−n+160)+0.05n=10.5

−0.05n+16=10.5(Simplify both sides of the equation)

−0.05n+16+−16=10.5+−16(Add -16 to both sides)

−0.05n=−5.5

−0.05n−0.05=−5.5−0.05(Divide both sides by -0.05)

n=110

Step: Substitute110fornind=−n+160:

d=−n+160

d=−110+160

d=50(Simplify both sides of the equation)

Answer:

d=50 and n=110


so there are 110 nickels