Last week, Emily paid 8.25 for x pounds of apples. This...

Last week, Emily paid $\$ 8.25$ for $x$ pounds of apples. This week she paid $\$ 9.50$ for $(x+1)$ pounds of apples. The price per pound was the same each week. How many pounds of apples did Emily buy each week and what was the price per pound? (Use $\frac{\text { total cost }}{\text { number of pounds }}=$ cost per pound for each week.)

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Key Concepts

Unit Rate Calculation

This concept involves finding a cost per unit, in this case, the price per pound of apples. It is determined by dividing the total cost by the total quantity purchased. This concept is crucial in comparing prices or establishing equivalency when the quantity changes.

Setting Up Rational Equations

In problems where the same rate is applied over different quantities, one sets up an equation by equating two instances of the unit rate. This involves creating fractions that represent the cost per unit for each scenario and then setting them equal to each other.

Solving Linear Equations

After setting up the rational equation, the next step is to solve for the unknown variable. This involves algebraic manipulation such as cross multiplication, combining like terms, and isolating the variable. Mastering these techniques helps in handling similar problems in algebra.

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