Math - mecca, Wednesday, October 24, 2007 at 9:20pm
Lauren has collected 150 nickels and dimes. She has 70 more nickels than dimes. How many nickels and how many dimes
Let x = # of dimes
x + (x + 70) = 150
2x + 70 = 150
2x = 80
x = 40 dimes
40 + 70 = 110 nickels
40 dimes
110 nickels
To solve this problem, we can set up a system of equations. Let's represent the number of nickels as "N" and the number of dimes as "D".
From the given information, we know that Lauren has 70 more nickels than dimes. So we can write the first equation as:
N = D + 70
We also know that Lauren has collected a total of 150 nickels and dimes. So the sum of the number of nickels and dimes should be equal to 150. We can write the second equation as:
N + D = 150
Now we can solve these equations to find the values of N and D.
From the first equation, we can substitute the value of N in terms of D into the second equation:
(D + 70) + D = 150
Simplifying the equation:
2D + 70 = 150
Subtracting 70 from both sides:
2D = 80
Dividing both sides by 2:
D = 40
So, Lauren has 40 dimes.
Now we can substitute this value of D back into the first equation to find the value of N:
N = 40 + 70
N = 110
Therefore, Lauren has 110 nickels and 40 dimes.