1.)Dylan has $2.30 and dimes and nickels The number of dimes exceeds the number of Nichols by five find the number he has a each.
2.) A coin purse contained $4.70 in Nickels and quarters there are 30 Coins in all how many of each kind of there.
3.) Margarita bought one cent stamps $.33 stamps and $.34 stamps for $22.45. The number of $.33 stamps was 10 less than twice the number of $.34 cent stamps. How many of each kind did she buy?
1
170
1.) To solve this problem, we need to set up a system of equations. Let's represent the number of dimes as "d" and the number of nickels as "n".
Given that Dylan has $2.30, we can write the equation:
0.10d + 0.05n = 2.30
We are also told that the number of dimes exceeds the number of nickels by five. Mathematically, this can be expressed as:
d = n + 5
Now we can solve the system of equations to find the values of "d" and "n".
First, let's substitute the value of "d" from the second equation into the first equation:
0.10(n + 5) + 0.05n = 2.30
Simplify the equation:
0.10n + 0.50 + 0.05n = 2.30
0.15n + 0.50 = 2.30
Subtract 0.50 from both sides:
0.15n = 1.80
Divide both sides by 0.15:
n = 12
Now substitute this value of "n" back into the second equation to find "d":
d = 12 + 5
d = 17
Therefore, Dylan has 17 dimes and 12 nickels.
2.) Let's represent the number of nickels as "n" and the number of quarters as "q".
According to the given information, there are 30 coins in total and the total value of the coins is $4.70. We can set up the following equations:
n + q = 30 (equation 1)
0.05n + 0.25q = 4.70 (equation 2)
Now, we can solve this system of equations to find "n" and "q".
Multiply equation 1 by 0.05 to have the same coefficient for "n":
0.05n + 0.05q = 1.50 (equation 3)
Subtract equation 3 from equation 2:
0.05n + 0.25q - (0.05n + 0.05q) = 4.70 - 1.50
0.20q = 3.20
Divide both sides by 0.20:
q = 16
Substitute this value of "q" into equation 1 to find "n":
n + 16 = 30
n = 30 - 16
n = 14
Therefore, there are 14 nickels and 16 quarters.
3.) Let's represent the number of 1-cent stamps as "x", the number of 33-cent stamps as "y", and the number of 34-cent stamps as "z".
According to the given information, the cost of 1-cent stamps is $0.01, the cost of 33-cent stamps is $0.33, and the cost of 34-cent stamps is $0.34. The total cost of all the stamps is $22.45. We can set up the following equations:
0.01x + 0.33y + 0.34z = 22.45 (equation 1)
y = 2z - 10 (equation 2)
Now, we can solve this system of equations to find "x", "y", and "z".
Substitute the value of "y" from equation 2 into equation 1:
0.01x + 0.33(2z - 10) + 0.34z = 22.45
Simplify the equation:
0.01x + 0.66z - 3.3 + 0.34z = 22.45
0.01x + 1z - 3.3 = 22.45
Combine like terms:
0.01x + 1.34z - 3.3 = 22.45
Rearrange the equation:
0.01x + 1.34z = 22.45 + 3.3
0.01x + 1.34z = 25.75 (equation 3)
Now, we have a system of two equations (equation 2 and equation 3) with two variables ("z" and "x").
Since we don't have an equation directly relating "x" and "z", we will need additional information to solve the system completely.