Lianne has nineteen coins worth $1.45. Some coins are dimes & the rest are nickels. How many dimes does she have.
I understand the D + N = 19 & the 10D + 5N = 145, but I don't understand how you'd subtract them from each other?
I answered that same question last night
divide the second equation by 5
2d + n = 29, now put the first underneath it
d + n = 19
subtract
d + 0 = 10
so there were 10 dimes, and from the first equation n=9
so there were 9 nickels
check: is 10+9 = 19 ? yes
value: 10 dimes = $1.00
9 nickels = 0.45
totol $1.45
5645323
To solve this problem, you need to use a system of equations. Let's break down the information given:
1. The total number of coins is 19: D + N = 19, where D represents the number of dimes and N represents the number of nickels.
2. The total value of these coins is $1.45: 10D + 5N = 145, where 10D represents the value of dimes (10 cents each) and 5N represents the value of nickels (5 cents each).
To calculate the number of dimes, you can subtract the first equation from the second equation. This will eliminate the variable N and leave you with an equation in terms of D, which you can then solve.
Let's perform the subtraction:
(10D + 5N) - (D + N) = 145 - 19
10D + 5N - D - N = 126
9D + 4N = 126
Now, you have a new equation: 9D + 4N = 126. You can solve this equation to determine the number of dimes (D) Lianne has.