Question

Three friends met for a book club at a coffee shop, each friend ordered a cup of coffee and two donuts. the total of the order was $22.00
a. if a cup of coffee is $3.25, then write a diagram to solve for the cost of the donut

3( 3.25 + x ) = 21.75

b.whats the donuts cost?

Answer 1

Answer:

$Cost\ of\ donut=\frac{49}{24}\approx \ 2.042\\\\cost\ of\ donuts=\frac{49}{4}\approx \ 12.25$

Step-by-step explanation:

a.

$Let\ cost\ of\ coffee=y\\\\cost\ of\ one\ donut=x\\\\Each\ friend\ buy\ one\ coffee\ and\ two\ donuts\\\\Amount\ for\ 1\ friend=Cost\ of\ coffee+2\times cost\ of\ donut\\\\Amount\ for\ 1\ friend=y+2x\\\\Amount\ required\ for\ 3\ friend=3\times Amount\ for\ 1\ friend\\\\Amount\ required\ for\ 3\ friend=3\times (y+2x)\\\\Amount\ required\ for\ 3\ friend=3y+6x\\\\Total\ bill=\ 22\\\\3y+2x=22\\\\Given\ cost\ of\ coffee=\ 3.25\\\\y=\ 3.25$

$Hence\ solution\ of\ following\ system\ of\ equation\ will\ give\ cost\ of\ donut:\\\\3y+6x=22\\\\y=3.25\\\\\\Substitute\ y=3.25\ in\ first\ equation\\\\3\times 3.25+6x=22\\\\9.75+6x=22\\\\6x=22-9.75\\\\6x=12.25\\\\x=\frac{12.25}{6}\\\\x=\frac{49}{24}\approx \ 2.042\\\\Cost\ of\ donut=\frac{49}{24}\approx \ 2.042$

See attached diagram.

b.

$Each\ friend\ takes\ 2\ donuts\\\\Total\ donuts=Number\ of\ friends\times 2\\\\Total\ donuts=3\times 2=6\\\\cost\ of\ donuts=number\ of\ donuts\times cost\ of\ 1\ donut\\\\cost\ of\ donuts=6\times \frac{49}{24}\\\\cost\ of\ donuts=\frac{49}{4}\approx \ 12.25$