MATH SOLVE

2 months ago

Q:
# Nicole has a job transporting soft drinks by truck. Her truck is filled with cans that weigh 14 ounces each and bottles that weigh 70 ounces each. There is a combined total of 980 cans and bottles in her truck. Let x be the number of 14 -ounce cans in her truck. Write an expression for the combined total weight (in ounces) of the cans and bottles in her truck.

Accepted Solution

A:

Answer:[tex]W_{total} = -56X + 68600[/tex]Step-by-step explanation:We wil define:1) "x" as number of cans inside the truck.2) "y" as number of bottles inside the truck.We now that the amount of both cans and bottles inside the truck is "980". This quantity is equal to the sum of cans and bottles, so now we can write: [tex]X+Y=980[/tex]We will call this expression equation n° 1.On the other hand, we know that the total weight is a sum of the weight of the cans and the weight of the bottles. The total weight of the cans, for example, is the result of multiplying the numbers of cans in the truck with the weight of each can, like here: ([tex]W_{cans} = X * 14 oz[/tex]So now we can write:[tex]W_{total} = (X*14oz) + (Y*70oz)[/tex]We well call this expression equation n° 2.From equation n°1 we obtain "y", like this:[tex]X + Y = 980\\Y = 980 - X[/tex]And we replace it in equation n°2:[tex]W_{total} = (X*14) + (Y * 70)\\\\W_{total} = 14X + 70Y\\W_{total} = 14X + 70(980-X)\\W_{total} = 14X + 68600 - 70X\\W_{total} = -56X + 68600[/tex]Now we have the expression of the total weight considering the amount of cans in the truck.*** IMPORTANT: there is a character similar to an "A" that i can't erase, maybe is a mistake from brainly. Do not consider it as part of the solution.