You and your friend are selling magazine subscriptions for a fundraiser. After w weeks, you have sold (3w+4) subscriptions and your friend has sold (5w+1) subscriptions.
a. Write an expression in simplest form that represents the difference between the number of subscriptions your friend has sold and the number you have sold.
An expression is
.
b. After 5 weeks, your friend has sold
more subscriptions than you.
a. The expression in simplest form that represents the difference between the number of subscriptions your friend has sold and the number you have sold is:
(5w + 1) - (3w + 4).
To simplify this expression, we can distribute the negative sign in front of (3w + 4) and combine like terms:
5w + 1 - 3w - 4.
Combining like terms, we get:
(5w - 3w) + (1 - 4) = 2w - 3.
Therefore, the simplified expression is 2w - 3.
b. After 5 weeks, your friend has sold more subscriptions than you. To verify this, we need to compare the number of subscriptions each of you sold.
For you: Substitute w = 5 into the expression 3w + 4:
3(5) + 4 = 15 + 4 = 19 subscriptions.
For your friend: Substitute w = 5 into the expression 5w + 1:
5(5) + 1 = 25 + 1 = 26 subscriptions.
Therefore, after 5 weeks, your friend has sold 26 subscriptions, which is 26 - 19 = 7 more subscriptions than you have sold.