How much of another coffee that costs P15.00 should the coffee shop mix with the first?

Question

A coffee is to be made that sells foe P25.00 by mixing two types of coffee.Ther coffee shop has 40mL of coffee that costs P30.00.How much of another coffee that costs P15.00 should the coffee shop mix with the first?

Answer 1

Let x ml be the amount of the other coffee that costs P15.

If 40 ml of the shop’s coffee costs P30, then 4 ml costs P3. If we take a fixed amount of money, P75, we can buy 100 ml of the shop’s coffee (25 times 4 ml because P75 is 25 times P3).

For the same cost we can buy 5x ml of the other coffee (because P75 is 5 times P15).

The mixture contains x+40 ml of coffee and for P75 we can buy 3(x+40) ml (because P75 is 3 times P25, the cost of the mixture).

So, we can equate these: 100+5x=3(x+40)=3x+120 ml for P75.

100+5x=3x+120, 2x=120-100=20 ml so x=10 ml.

Therefore we need 10 ml of the other coffee to get the mixture at a cost of P25.

By the way, 75 is the LCM of 3, 15 and 25.

QUICK CHECK

100ml for P75⇒40ml for 40/100×75=P30

50ml for P75⇒10ml for 10/50×75=P15

150ml for P75⇒50ml for 50/150×75=P25