Question

Naomi spent $84 on 4 chairs and 3 tables. At the same store, Juan bought 5 tables and 8 chairs and spent $151. Does the system of equations below model this situation?

4c+3t=84
5t−8c=151
a) Yes
b) No
c) Insufficient information
d) Can't be determined

Answer 1

The system of equations 4c+3t=84 and 5t−8c=151 does not accurately model the given situation. Therefore, the correct option is c) Insufficient information.

Step-by-step explanation:

The system of equations 4c+3t=84 and 5t−8c=151 does not model the situation accurately. To determine if the system models the situation, we can solve the equations to find if there is a solution that satisfies both equations. However, when we solve these equations, we get contradictory results. Substituting the value of t from the first equation into the second equation, we get: 5(84-4c)-8c=151, which simplifies to 420-20c-8c=151. Combining like terms, we have -28c=151-420, which further simplifies to -28c=-269. This leads to a contradiction, as c is not a real number.