Troy and Lisa were shopping for school supplies. Each purcahsed different quantities of the same notebook and thumb drive. Troy bought five notebooks and four thumb drives for $83. Lisa bought six notebooks and six thumb drives for $120. Find the cost of each notebook and each thumb drive.
Let's assume the cost of each notebook is "N" and the cost of each thumb drive is "D".
From the problem, we have the following information:
Troy bought 5 notebooks and 4 thumb drives for $83:
5N + 4D = 83
Lisa bought 6 notebooks and 6 thumb drives for $120:
6N + 6D = 120
Now we have a system of two equations. We can use either substitution or elimination method to find the values of N and D.
Let's use the elimination method to solve the system:
Multiply the first equation by 6 and the second equation by 5 to make the coefficients of "N" equal:
(6)(5N + 4D) = (6)(83) becomes 30N + 24D = 498
(5)(6N + 6D) = (5)(120) becomes 30N + 30D = 600
Now subtract the second equation from the first equation:
(30N + 24D) - (30N + 30D) = 498 - 600 simplifies to -6D = -102
Divide both sides of the equation by -6:
-6D / -6 = -102 / -6 simplifies to D = 17
Now substitute the value of D back into one of the original equations to solve for N:
5N + 4(17) = 83
5N + 68 = 83
Subtract 68 from both sides of the equation:
5N = 83 - 68
5N = 15
Divide both sides of the equation by 5:
5N / 5 = 15 / 5
N = 3
Therefore, the cost of each notebook (N) is $3 and the cost of each thumb drive (D) is $17.
To solve this problem, we can set up a system of equations. Let's let the cost of each notebook be represented by 'n' and the cost of each thumb drive be represented by 't'.
From the given information, we know:
Troy bought 5 notebooks and 4 thumb drives for $83, so the equation is:
5n + 4t = 83
Lisa bought 6 notebooks and 6 thumb drives for $120, so the equation is:
6n + 6t = 120
Now we can solve the system of equations using the method of substitution or elimination.
Let's start by using the method of elimination. We'll multiply the first equation by 6 and the second equation by 5 to make the coefficients of 'n' the same:
6 * (5n + 4t) = 6 * 83
5 * (6n + 6t) = 5 * 120
This simplifies to:
30n + 24t = 498
30n + 30t = 600
Next, we can subtract the second equation from the first equation to eliminate 'n':
(30n + 24t) - (30n + 30t) = 498 - 600
Simplifying this gives:
-6t = -102
Dividing both sides of the equation by -6, we get:
t = 17
Now that we know the cost of each thumb drive is $17, we can substitute this value back into one of the original equations to solve for 'n'.
Let's use the first equation:
5n + 4t = 83
5n + 4(17) = 83
Simplifying this gives:
5n + 68 = 83
Subtracting 68 from both sides:
5n = 83 - 68
5n = 15
Dividing both sides of the equation by 5, we get:
n = 3
Therefore, the cost of each notebook is $3, and the cost of each thumb drive is $17.
5n + 4t = 83
6n + 6t = 120 ... n + t = 20 ... 4n + 4t = 80
subtracting equations ... n = 3
substitute back to find t