Final answer:
The price of each item was calculated using a system of equations derived from Steven and Jennifer's purchases. The elimination method was used to find that each t-shirt is $28 and each keychain is $18.
Step-by-step explanation:
To solve the problem of finding the price of each item (t-shirts and keychains) from the purchases made by Steven and Jennifer, we can set up a system of equations based on the given information. Let T be the price of one t-shirt and K be the price of one keychain.
Setting up the Equations
Steven's purchase: 3T + 2K = $120
Jennifer's purchase: 5T + 4K = $212
We can use substitution or elimination method to solve this system of equations. For simplicity, let's use the elimination method.
Elimination Method
We can multiply Steven's equation by 2 to align the keychain variable with Jennifer's equation:
6T + 4K = $240 (Steven's equation multiplied by 2)
5T + 4K = $212 (Jennifer's equation)
Now we subtract Jennifer's equation from the modified Steven's equation:
(6T + 4K) - (5T + 4K) = $240 - $212
T = $28
Now we know that the price of each t-shirt is $28, we can substitute T in one of the original equations to find K:
3T + 2K = $120
3($28) + 2K = $120
$84 + 2K = $120
2K = $120 - $84
2K = $36
K = $18
Therefore, each t-shirt is $28 and each keychain is $18.