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together Tom and Jared sell 85 cups of hot chocolate at the football game. Jared sells 7 more cups than Tom. How many do they each sell?
Can you show work
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Solution 1. One equation in one unknown
Let T = the number of cups Tom sold.
Then the number of cups Jared sold was (85-T).
The condition says that
(85-T) = T + 7.
Simplify and solve:
85 - T = T + 7 ---> 85 - 7 = 2T ---> 2T = 78 ---> T = = 39.
Answer. Tom sold 46 cups. Jared sold T + 7 = 39 + 7 = 46.
Solution 2. The system of two equations in two unknowns.
Let T = the number of cups Tom sold,
J = the number of cups Jared sold.
The condition says
J + T = 85, (1)
J - T = 7. (2)
Add equations (1) and (2). You will get
2J = 85 + 7 ---> 2J = 92 ---> J = = 46.
You get the same answer.
Solved.