sam has $3.50 in dimes and quarters. he has 23 quarters all together. how many of each does he have?
will has $2.40 in dimes and nickels. he has 30 coins all together. how many of each does he have?
1. Your prob. says sam has 23qtrs,but
I'm assuming you meant 23 coins; he can't have 23 qtrs if he only has 3.50.
x dimes, y qtrs,
Eq1: x + y = 23 coins,
0.10x + 0.25y = 3.50,
Multiply both sides by 20:
Eq2: 2x + 5y = 70.
Solve the 2 Eqs:
x + y = 23,
2x + 5y = 70,
Multiply the 1st Eq by -2:
-2x -2y = -46,
2x + 5y = 70,
Add the 2 Eqs:
3y = 24,
y = 8 Qtrs.
Substitute 8 for y in EQ1:
X + 8 = 23,
X = 23 - 8,
X = 15 Dimes.
2. Same procedure as prob. 1.
Let's solve the problem step-by-step.
1. Sam has a total of $3.50 in dimes and quarters.
2. Let's assign variables to represent the number of dimes and quarters Sam has. Let's say 'd' represents the number of dimes and 'q' represents the number of quarters.
3. We know that the total value of the dimes is 10 cents each, while the total value of the quarters is 25 cents each.
4. Sam has a total of 23 quarters. So we can write the equation:
q = 23
5. The total value of the dimes and quarters is $3.50. We can write the equation as follows:
0.10d + 0.25q = 3.50
6. Now, we can substitute the value of 'q' from equation 4 into equation 5:
0.10d + 0.25(23) = 3.50
7. Simplifying this equation, we get:
0.10d + 5.75 = 3.50
8. Subtracting 5.75 from both sides of the equation, we get:
0.10d = 3.50 - 5.75
0.10d = -2.25
9. Dividing both sides of the equation by 0.10, we get:
d = -2.25 / 0.10
d = -22.5
10. Since the number of dimes cannot be negative, there is no solution to this problem. It seems there might be a mistake or some missing information.
Moving on to the next problem:
1. Will has a total of $2.40 in dimes and nickels.
2. Let's assign variables to represent the number of dimes and nickels Will has. Let's say 'd' represents the number of dimes and 'n' represents the number of nickels.
3. We know that the total value of the dimes is 10 cents each, while the total value of the nickels is 5 cents each.
4. Will has a total of 30 coins. So we can write the equation:
d + n = 30
5. The total value of the dimes and nickels is $2.40. We can write the equation as follows:
0.10d + 0.05n = 2.40
6. Now, we can solve the system of equations using the substitution method. From equation 4, we know that n = 30 - d. Substituting this into equation 5, we get:
0.10d + 0.05(30 - d) = 2.40
0.10d + 1.5 - 0.05d = 2.40
7. Simplifying this equation, we get:
0.05d + 1.5 = 2.40
8. Subtracting 1.5 from both sides of the equation, we get:
0.05d = 2.40 - 1.5
0.05d = 0.90
9. Dividing both sides of the equation by 0.05, we get:
d = 0.90 / 0.05
d = 18
10. Substituting the value of d into equation 4, we find:
n = 30 - 18
n = 12
Therefore, Will has 18 dimes and 12 nickels.
To find the number of dimes and quarters Sam has, you can use a system of equations.
Let's assume the number of dimes Sam has is "d" and the number of quarters he has is "q".
From the information given, we know two things:
1. The total value of Sam's coins is $3.50, which can be expressed as the equation: 0.10d + 0.25q = 3.50.
(Note: The value of a dime is $0.10, and the value of a quarter is $0.25.)
2. The total number of quarters Sam has is 23, so we can write another equation: q = 23.
Now we can solve this system of equations to find the values of "d" and "q".
1. Substitute the value of "q" from the second equation into the first equation:
0.10d + 0.25(23) = 3.50.
2. Simplify the equation:
0.10d + 5.75 = 3.50.
3. Subtract 5.75 from both sides of the equation:
0.10d = 3.50 - 5.75.
4. Simplify further:
0.10d = -2.25.
5. Divide both sides of the equation by 0.10 to isolate "d":
d = -2.25 / 0.10.
6. Calculate the value of "d":
d = -22.5.
Now, we have found that the number of dimes, "d," is -22.5, which doesn't make sense in this context.
There seems to be an error or inconsistency in the given information for Sam's problem. Please double-check the values provided.
If you have any other questions or need further clarification, feel free to ask!