Every night when Samantha came home from work she put any change she had in her pockets into a jar. One day she wanted to know how much change she had in her jar. She noticed that she had two more nickels than twice the number of dimes, and eight fewer quarters than twice the number of nickels. If the value of the quarters was $1.60 more than four times the value of the nickels and dimes together, what was the total value of the change in Samantha's jar?
plese help
just start writing down the facts as math.
n = 2d+2
eight fewer quarters than twice the number of nickels
q = 2n-8
value of the quarters was $1.60 more than four times the value of the nickels and dimes together
25q = 4(10d+5n)+160
Putting all that together, we have
n = 2d+2
q = 2n-8
25q = 4(10d+5n)+160
substituting in for q and n in the last equation, we have
25(2(2d+2)-8) = 4(10d+5(2d+2))+160
d=15
So, now you know how many dimes there are, and you can figure out the other coins.
I. Need help in math
To solve this problem, let's break it down and find the values of each type of coin.
Let's assume that Samantha had:
- x number of dimes
- 2x + 2 number of nickels (two more nickels than twice the number of dimes)
- 2(2x + 2) - 8 number of quarters (eight fewer quarters than twice the number of nickels)
To find the value of each type of coin, we need to know their worth in cents.
Dimes are worth 10 cents each, so the worth of all the dimes is 10x cents.
Nickels are worth 5 cents each, so the worth of all the nickels is (2x + 2) * 5 cents.
Quarters are worth 25 cents each, so the worth of all the quarters is (2(2x + 2) - 8) * 25 cents.
According to the problem, the value of the quarters is $1.60 more than four times the value of the nickels and dimes together. So we can write the equation:
(2(2x + 2) - 8) * 25 = (4x + 2) * 5 + $1.60 * 100
Now, let's solve the equation for x:
50x + 50 - 200 = 20x + 10 + 160
30x = 300
x = 10
Now that we know x (the number of dimes), we can find the number of nickels and quarters.
Number of nickels = 2x + 2 = 2 * 10 + 2 = 22
Number of quarters = 2(2x + 2) - 8 = 2(2 * 10 + 2) - 8 = 44
Finally, to find the total value of the change in Samantha's jar, we can calculate the worth of each type of coin and add them together:
Worth of dimes = 10x = 10 * 10 = 100 cents
Worth of nickels = (2x + 2) * 5 = 22 * 5 = 110 cents
Worth of quarters = (2(2x + 2) - 8) * 25 = 44 * 25 = 1100 cents
Total value of the change in Samantha's jar = Worth of dimes + Worth of nickels + Worth of quarters
= 100 + 110 + 1100
= 1310 cents
So, the total value of the change in Samantha's jar is 1310 cents.