Question

You are selling tickets to a play. You have sold (3t+2) tickets for $5 each and (2t+5) tickets for $7 each. Write an expression that represents the total number of tickets sold so far. Then simplify the expression.

Answer 1

Given that the number of tickets that are sold for $5 is (3t+2) tickets.

The number of tickets that are sold for $7 is (2t+5) tickets.

We need to determine the expression that represents the total number of tickets sold and the simplified expression.

Total number of tickets sold:

The expression for (3t+2) tickets sold for $5 is given by

`5(3t+2)`

The expression for (2t+5) tickets sold for $7 is given by

`7(2t+5)`

The expression for the total number of tickets sold is given by

`5(3t+2)+7(2t+5)`

Thus, the expression that represents the total number of tickets sold is
`5(3t+2)+7(2t+5)`

Simplified expression:

We need to simplify the expression
`5(3t+2)+7(2t+5)`

Hence, let us multiply the terms within the bracket.

Thus, we get;

`15t+10+14t+35`

Adding the like terms, we have,

`29t+45`

Thus, the simplified expression is
`29t+45`