Problem Solving ( using linear equations)

[jhong213]

There were two in my homework that I've been stuck on for the past 30 minutes and i just couldn't find the correct equations or at least i got one of the two equations right so here they are:

1) Kayla has 25 ounces of a 75% boric acid solution.
How many ounces of 35% boric acid solution
should she add to obtain a solution that is
60% boric acid?

2) Hollis is paying off two student loans. One loan
charges 7% interest per year. The other loan
charges 9% interest per year. He owes $1500 more
on the 7% loan than he does on the other. Last year
he paid a total of $617 interest. How much does he
owe on each loan?

thank you

 

[mmm4444bot]

x = ounces of required 35% solution

The final mixture will be x + 25 ounces, right?

60% of those ounces are acid; the rest is water.

So, the amount of acid in the final mixture is expressed as 0.6(x + 25).

Where did this amount of acid come from? It came from the two donor solutions.

The amounts of acid (in each of the donor solutions) are 0.75(20) and 0.35x, right?

The sum of the donor acids must equal the acid in the final mixture, so there is your equation.

On exercise (2), if the question is asking for two loan balances on which combined $617 simple interest was charged after one year, that is easy enough.

The given information tells us the balance of the 7% loan in terms of the other balance, so it makes sense to pick a variable for the other balance.

x = the 9% loan balance

This way, we can express the first balance in terms of x.

x + 1500 = the 7% loan balance

Now we can express the interest charged on the 7% loan as 0.07(x + 15) and the interest charged on the 9% loan as 0.09x .

You know what the sum of these two interest amounts are, so there is your equation.

Please show some work, if you want more help.

Cheers ~ Mark