# Word Problems

## Cost of \$n\$ items

The Mathscribe Fruit Stand sells apples for \\$2 each. Let’s use the variable \$a\$ for the number of apples you want to buy. For each of the values of \$a\$ shown in the table below, how much would it cost to buy \$a\$ apples at the fruit stand?

\$a\$ = number of applescost of \$a\$ apples

If each apple costs \\$2, then the cost of \$a\$ apples = \$2a\$.

The Mathscribe Fruit Stand also sells bananas. They cost \\$3 each. For each of the values of \$b\$ shown in the table below, how much would it cost to buy \$b\$ bananas?

\$b\$ = number of bananascost of \$b\$ bananas
 What is an expression for the cost of \$b\$ bananas?

## More than one variable

Let’s say you want to buy \$a\$ apples and \$b\$ bananas at the same time. Since apples cost \\$2 each and bananas cost \\$3 each, the total amount of money you’ll spend is \$2a+3b\$. This is pictured on the grid to the left; the \$a\$ rectangles in the farther-left stack (with a width of 2) represent the cost of \$a\$ apples, while the \$b\$ rectangles in the farther-right stack (with a width of 3) represent the cost of \$b\$ bananas.

For each row of the table below, fill in the value of this expression for the given number of apples and bananas.

\$a\$ = number of apples
\$b\$ = number of bananas
\$2a+3b\$ = cost of apples and bananas
 The Mathscribe Fruit Stand has moved to the tropics. They are now selling coconuts for \\$4 each, and dates for \\$5 each. This is pictured on the grid to the left, as in multiqn. If you want to buy \$c\$ coconuts and \$d\$ dates, what is an expression for the total amount of money you will spend?

For each row of the table below, fill in the amount of money you need to spend if you want to buy \$c\$ coconuts and \$d\$ dates.

\$c\$ = number of coconuts
\$d\$ = number of dates
\$4c+5d\$ = total cost

You want to buy \$a\$ apples, \$b\$ bananas, and \$d\$ dates from the fruit stand. As before, apples cost \\$2, bananas cost \\$3, and dates cost \\$5. You would also like to buy a basket to hold your fruit, which costs \\$8. An expression for the total amount of money you need to spend to do all this is \$2a+3b+5d+8\$.

This is pictured on the grid to the left, with the leftmost stack of rectangles representing the cost of \$a\$ apples, the next stack representing the cost of \$b\$ bananas, the next stack representing the cost of \$d\$ dates, and the rectangle on the right representing the price of the basket.

For each row of this table, what is the total amount you will be spending?

\$a=\$ number of apples
\$b=\$ number of bananas
\$d=\$ number of dates
\$2a+3b+5d+8\$ = total cost