Chapter 7, Problem 22PTTS

a.

To determine

To list: All possible ways that you can buy exactly $80$ granola bars.

Answer to Problem 22PTTS

The possible ways of buying granola is $4\text{ boxes of 20 granola}$ , $\text{5 boxes of 8 granola and 2 boxes of 20 granola}$ , $\text{10 boxes of 8 granola}$ .

Explanation of Solution

Given information: A store sells granola bars in boxes of $8$ and $20$ . A box of $8$ bars costs $\$3.12$ and a box of $20$ bars costs $\$7$ .

Calculation: Since, I want to buy exactly $80$ granola bars.

Let’s see all the possible ways of buying exactly $80$ granola,

  $\Rightarrow 8x+20y=80$

The all possible values of $x\text{ and }y$ is $\left(0,4\right),\left(5,2\right),\left(10,0\right)$

Hence, The possible ways of buying granola is $4\text{ boxes of 20 granola}$ , $\text{5 boxes of 8 granola and 2 boxes of 20 granola}$ , $\text{10 boxes of 8 granola}$ .

To determine

To find: How should you buy exactly $80$ granola bars if you spend the least amount of money.

Answer to Problem 22PTTS

The amount to buy exactly $80$ is $\$28$ and the combination granola is $4\text{ boxes of 20 granola}$ .

Explanation of Solution

Given information: A store sells granola bars in boxes of $8$ and $20$ . A box of $8$ bars costs $\$3.12$ and a box of $20$ bars costs $\$7$ .

Calculation: Since, The possible ways of buying granola is $4\text{ boxes of 20 granola}$ , $\text{5 boxes of 8 granola and 2 boxes of 20 granola}$ , $\text{10 boxes of 8 granola}$ .

Let’s see the combination of granola which is of least amount,

The cost of $4\text{ boxes of 20 granola }=4\times \$7=\$28$

The cost of $\text{5 boxes of 8 granola and 2 boxes of 20 granola}=5\times \$3.12+2\times \$7=\$29.6$

The cost of $\text{10 boxes of 8 granola}=10\times \$3.12=\$31.2$

Hence, The amount to buy exactly $80$ is $\$28$ and the combination granola is $4\text{ boxes of 20 granola}$ .