Mia has a jar containing nickels and dimes worth $4.80\$4.80 in total. If she has 1212 more dimes than nickels, how many of each coin does she have?

N i c k e l s = 24 ; D i m e s = 36 Nickels=24;Dimes=36

Mia has a jar containing nickels and dimes worth $ 4.80 \$4.80 in total. If she has 12 12 more dimes than nickels, how many of each coin does she have?

this problem, Mia has a jar containing nickels and dimes that in total are worth $4.80. And, we know that she has 12 more dimes than nickels, and we want to know how many of each coin she has. So, to better understand this problem, let's draw a picture. Here's her jar, which we know totals $4.80. And, we know that the contents of this jar are part nickels and part dimes. We also know that she has 12 more dimes than nickels, which means that there is a greater number of dimes in this jar than there are nickels. So now that we understand the problem, let's build our equation. We can already see how this equation is going to be set up using our diagram. We have a total amount that is going to be equal to the sum of our partial amounts. So if I wanted to calculate $4.80 out of some amount of nickels and some amount of dimes, I would take my $4.80, and I would find them by taking the number of nickels I have and multiplying it by their value in dollars, which is 0.05, and I would add to that the number of dimes I have multiplied by their value in dollars, which is 0.1. Now that we have our equation, we're ready to start solving. In order to solve this, we need to get it in terms of one variable, whereas here we have two variables. So, we need to take a closer look at our relationship between our nickels and our dimes. We know that there are 12 more dimes than nickels. I could express this algebraically as the number of dimes we have is equal to the number of nickels we have plus an additional 12. And now that I have d in terms of n, I can go ahead and take n plus 12, and substitute that in for d in my equation. Doing that, we get 4.8 is equal to n times 0.05, plus n plus 12, times 0.1. Now, we're ready to solve for n. We're going to simplify by distributing in the 0.1, so we have 4.8 is equal to n times 0.05, plus n times 0.1, plus 12 times 0.1, is 1.2. Now we're ready to collect all variable terms to one side, and all other terms to the other side. So we're going to subtract 1.2 from both sides, and 4.8 minuteus 1.2 is 3.6, and n times 0.05 plus n times 0.1 is n times 0.15. And next, we isolate by dividing both sides by 0.15, and we get that n is equal to 24. So the number of nickels we have is 24 nickels. And to find the number of dimes we have, we're going to take our number of nickels and we're going to add 12 to them. So we get that our number of dimes is 36.

Mia has a jar containing nickels and dimes worth $ 4.80 \$4.80 in total. If she has 12 12 more dimes than nickels, how many of each coin does she have?

N i c k e l s = 24 ; D i m e s = 36 Nickels=24;Dimes=36

N i c k e l s = 36 ; D i m e s = 24 Nickels=36;Dimes=24

N i c k e l s = 30 ; D i m e s = 42 Nickels=30;Dimes=42

N i c k e l s = 42 ; D i m e s = 30 Nickels=42;Dimes=30

3. Solving Word Problems

Mixture Problem Solving

Beginning & Intermediate Algebra

3. Solving Word Problems

Mixture Problem Solving

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Multiple Choice

Mia has a jar containing nickels and dimes worth $dollar sign 4.80$ in total. If she has $12$ more dimes than nickels, how many of each coin does she have?

$N i c k e l s = 36; D i m e s = 24$

$N i c k e l s = 24; D i m e s = 36$

$N i c k e l s = 30; D i m e s = 42$

$N i c k e l s = 42; D i m e s = 30$

Verified step by step guidance

Define variables: Let $N$ represent the number of nickels and $D$ represent the number of dimes Mia has.

Translate the problem statement into equations: Since Mia has 12 more dimes than nickels, write the equation $D = N + 12$.

Express the total value of the coins in cents: Each nickel is worth 5 cents and each dime is worth 10 cents. The total value is 480 cents (since \$4.80 = 480$ cents). So, write the equation $5N + 10D = 480$.

Substitute the expression for $D$ from the first equation into the value equation: Replace $D$ with $N + 12$ in \$5N + 10D = 480$ to get $5N + 10(N + 12) = 480$.

Solve the resulting equation for $N$, then use the value of $N$ to find $D$ using $D = N + 12$.

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