A store is having a sale on chocolate chips and walnuts. For 2 pounds of chocolate chips and 5 pounds of walnuts, the total cost is \( \$ 18 \). For 8 pounds of chocolate chips and 3 pounds of walnuts, the total cost is \( \$ 21 \). Find the cost for each pound of chocolate chips and each pound of walnuts. Cost for each pound of chocolate chips: \( 5 \square \)

Let \( x \) be the cost per pound of chocolate chips and \( y \) be the cost per pound of walnuts. We can set up the following equations based on the information given: 1. \( 2x + 5y = 18 \) (for 2 pounds of chocolate chips and 5 pounds of walnuts) 2. \( 8x + 3y = 21 \) (for 8 pounds of chocolate chips and 3 pounds of walnuts) To solve these equations, we can use substitution or elimination. Let's use the elimination method. From the first equation, we can express \( y \) in terms of \( x \): \[ y = \frac{18 - 2x}{5} \] Substituting this expression into the second equation: \[ 8x + 3\left(\frac{18 - 2x}{5}\right) = 21 \] Multiplying through by 5 to eliminate the fraction: \[ 40x + 3(18 - 2x) = 105 \] Expanding and combining like terms: \[ 40x + 54 - 6x = 105 \] \[ 34x + 54 = 105 \] \[ 34x = 51 \] \[ x = \frac{51}{34} \] \[ x \approx 1.50 \] Now subbing \( x \) back into the equation for \( y \): \[ y = \frac{18 - 2\left(\frac{51}{34}\right)}{5} \] Calculating this gives: \[ y = \frac{18 - \frac{102}{34}}{5} \] \[ y = \frac{18 - 3}{5} \approx \frac{15}{5} = 3 \] So the final costs are approximately: Cost for each pound of chocolate chips: \( 1.50 \) Cost for each pound of walnuts: \( 3.00 \) There you go! You've successfully found the rates per pound. Now you can splurge at the bakery without breaking the bank! Happy baking!