5n + 4t = 83
6n + 6t = 120 ... n + t = 20 ... 4n + 4t = 80
subtracting equations ... n = 3
substitute back to find t
6n + 6t = 120 ... n + t = 20 ... 4n + 4t = 80
subtracting equations ... n = 3
substitute back to find t
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.
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.