Question

system of equation word problem;
Mark only has dimes and nickles in his car. He has 21coins that value $1.50. How many dimes and how many nickels does he have in his car?

Answer 1

You first have to assign variables. I will assign the number to dimes to the variable D. I will also assign the number of nickels to the variable N. To write the first equation we will use the fact that Mark has only 21 coins. So the number of dimes and the number of nickels must equal 21.==> D+N=21 is our first equation. The next equation is the amount of money Mark has. A dime is worth $0.10 and a nickel is worth $0.05. So we multiple both variables by how much they are worth. The second equation is $0.10D+$0.05N=$1.25. We now have our two equations. Now we can solve our equations.

D+N=21
.10D+.05N=1.25

I plan on using the substitution method to solve this problem. I will solve the first equation for D. So I subtract N from both sides. D=21-N. I will plug this into the second equation.
.10(21-N)+.05N=1.25
I then distribute .10===> (2.1-.10N) + .05N=1.25
I will then combine like terms (N). -.10N+.05N=-.05N
Our equation reduces to 2.1-.05N=1.25.
Now we subtract 2.1 from both sides.===> -.05N=-.85
Then divide by -.05 on both sides. N= 17. So we have 17 nickels. Since we have 21 coins and we know that 17 coins are nickels then 4 coins must be dimes.

Answer 2

thanks that was a perfectly good explanation!!!!!!!!!!!!!!!!!