Rita would like to change a $10 bill into dimes and quarters. she wants to have 12 more quarters than dimes.how many of each should receive?
do t in pennies
1000 = 10 x + 25 y
y = x + 12
Well, Rita is really aiming for some spare change, isn't she? Let's help her out by solving this peculiar math puzzle.
Let's assume Rita receives "x" dimes. According to the problem, she wants 12 more quarters than dimes. So, she would receive (x + 12) quarters.
Now, let's calculate the total value of the coins. We know that each dime is worth $0.10, and each quarter is worth $0.25. Rita wants to change a $10 bill, so the equation is:
0.10x + 0.25(x + 12) = 10
Simplifying this equation gives us:
0.10x + 0.25x + 3 = 10
0.35x = 7
x = 20
So, Rita should receive 20 dimes and (20 + 12) = 32 quarters.
Now she can jingle and jangle her way through town with 20 dimes and 32 quarters – talk about making a lot of noise!
Let's solve this step-by-step:
Step 1: Assign Variables
Let's assign variables to the quantities we are trying to find. Let "x" represent the number of dimes and "x + 12" represent the number of quarters.
Step 2: Write an Equation for the Total Value
The total value of the coins must equal $10. Since a dime is worth $0.10 and a quarter is worth $0.25, we can write the equation:
(0.10x) + (0.25(x + 12)) = 10
Step 3: Solve the Equation
Multiply the decimal values by 100 to eliminate decimals:
10x + 25(x + 12) = 1000
Simplify and solve the equation:
10x + 25x + 300 = 1000
35x + 300 = 1000
35x = 1000 - 300
35x = 700
x = 700 / 35
x = 20
Step 4: Calculate the Number of Quarters
Now that we know x = 20, we can substitute it back into our equation to find the number of quarters:
x + 12 = 20 + 12 = 32
Therefore, Rita should receive 20 dimes and 32 quarters in order to have a total value of $10, with 12 more quarters than dimes.
To solve this problem, we can use algebraic equations. Let's start by assigning variables to the unknown quantities.
Let's say the number of dimes is represented by 'x'. Since Rita wants to have 12 more quarters than dimes, the number of quarters would be represented by 'x + 12'.
The value of each dime is $0.10, and the value of each quarter is $0.25. So, the total value of the dimes can be written as 0.10x, and the total value of the quarters is 0.25(x + 12).
Since the total value doesn't change when we convert the $10 bill, we can set up the following equation:
0.10x + 0.25(x + 12) = 10
Solving this equation will give us the number of dimes and quarters Rita should receive. Let's do the math to find the solution:
0.10x + 0.25x + 3 = 10
0.35x = 7
x = 7 / 0.35
x = 20
So, Rita should receive 20 dimes and 20 + 12 = 32 quarters to convert her $10 bill into dimes and quarters.