Question 8573
Let T be the number of kilos of hard candy.
Let L be the number of kilos of chewy candy. Actually, they gave you that. There are 12 kilos of chewy candies.


Fact: When you mix the two together, the new mixture will weigh T + 12 kilos.


We know that we have 12 kilos of chewy candy that is worth PhP 240 per kilo. So we have PhP 2880 worth of chewy candy. We want to add an unknown amount of hard candy (T kilos) and we know that it costs PhP 210 per kilo. So, we'll take the PhP 2880 and add 210*T to it. So far, our equation should be {{{ 2880 + 210T }}}.


Alright. We already said that the weight of the new mixture is T + 12 kilos. They told us that the new mixture sells for PhP 230 per kilo. So the new mixture will have a total cost of 230(T + 12). We then say {{{ 2880 + 210T = 230(T+12) }}} because combining the hard candy and the soft candy with their prices is equal to the price per kilo of the new mixture, times the weight of the new mixture.


{{{ 2880 + 210T = 230(T+12) }}} <----- Start here.


{{{ 2880 + 210T = 230T + 2760 }}} <---- Distribute.


{{{ 120 = 20T }}} <---- Two steps in 1: subtracted 2760 from both sides and subtracted 210T from both sides.


{{{ 6 = T }}} <----- Divide both sides by 20. We end up with 6 kilos. This means that we MUST have 6 kilos of hard candy so that when mixed with the chewy candy, the mixture will be worth PhP 230 per kilo.