Question

Cherries cost ​$4​/lb. Grapes cost ​$2.50​/lb. You can spend no more than ​$15 on​ fruit, and you need at least 5 lb in all. Create a graph showing the amount of each fruit you can buy.

Answer 1

The quantity of cherries bought is 1.67 lb

The quantity of grapes bought is 3.33 lb

Explanation:

Given as :

The cost of cherries = $4 per lb

The cost of grapes = $2.50 per lb

Total money spend on fruits = $15

The quantity of both fruits to bought = 5 lb

Let The quantity of cherries bought = c lb

Let The quantity of grapes bought = g lb

Now, According to question

quantity of both fruits to bought = quantity of cherries bought + quantity of grapes bought

i.e c + g = 5 lb ........1

And

Total money spend on fruits = cost of cherries × quantity of cherries bought + cost of grapes × quantity of grapes bought

Or , c lb × $4 per lb + g lb × $2.50 per lb = $15

Or, 4 c + 2.50 g = 15 .......2

Now, Solving equation 1 and 2

So, (4 c + 2.50 g) - 2.50 × (c + g) = 15 - 5 × 2.50

Or, (4 c - 2.50 c) + (2.50 g - 2.50 g) = 15 - 12.50

Or, 1.5 c + 0 = 2.5

∴ c =
`(2.5)/(1.5)`

I.e c = 1.67 lb

So, The quantity of cherries bought = c = 1.67 lb

Putting the value of c in eq 1

Since , c + g = 5 lb

Or, g = 5 lb - c

Or, g = 5 lb - 1.67 lb

i.e g = 3.33 lb

So, The quantity of grapes bought = g = 3.33 lb

Hence, The quantity of cherries bought is 1.67 lb

and The quantity of grapes bought is 3.33 lb Answer