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

Answer:

The quantity of cherries bought is 1.67 lb

The quantity of grapes bought is 3.33 lb

Step-by-step 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 = $\dfrac{2.5}{1.5}$

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