at a cafe, the bishop family pays $12 for a salad, a fruit bowl, and two sandwiches. the cortez family pays…

at a cafe, the bishop family pays $12 for a salad, a fruit bowl, and two sandwiches. the cortez family pays $14 for two salads and two sandwiches. the donovan family pays $14 for a salad and three fruit bowls. what is the price of a fruit bowl at the cafe?\n$2\n$3\n$4\n$5

at a cafe, the bishop family pays $12 for a salad, a fruit bowl, and two sandwiches. the cortez family pays $14 for two salads and two sandwiches. the donovan family pays $14 for a salad and three fruit bowls. what is the price of a fruit bowl at the cafe?\n$2\n$3\n$4\n$5

Answer

Explanation:

Step1: Set up equations

Let $s$ be the price of a salad, $f$ be the price of a fruit - bowl, and $w$ be the price of a sandwich. The Bishop family's purchase gives the equation $s + f+2w = 12$. The Cortez family's purchase gives the equation $2s + 2w=14$. The Donovan family's purchase gives the equation $s + 3f=14$.

Step2: Simplify the Cortez - family equation

From $2s + 2w = 14$, we can divide by 2 to get $s + w=7$, then $w = 7 - s$.

Step3: Substitute into the Bishop - family equation

Substitute $w = 7 - s$ into $s + f+2w = 12$: [ \begin{align*} s + f+2(7 - s)&=12\ s + f + 14-2s&=12\ f - s&=- 2\ s&=f + 2 \end{align*} ]

Step4: Substitute into the Donovan - family equation

Substitute $s=f + 2$ into $s + 3f=14$: [ \begin{align*} f + 2+3f&=14\ 4f&=12\ f&=3 \end{align*} ]

Answer:

$3$