Math CentralQuandaries & Queries


Question from Sandra, a student:

I have two questions. Please solve both. Thank you.

1.) In your chemistry class, you have a bottle of 5% boric acid solution and a bottle of 2% boric acid solution. You need 60 milliliters of a 3% boric acid for an experiment. How much of each solution do you need to mix them together?

2.) You plant a 14-inch hemlock tree in your backyard that grows at a rate of 4 inches per year and an 8 inch blue spruce that grows at a rate of 6 inches per year. In how many years after you plant the trees will the trees be the same height? How tall will each tree be?

Thank you. I did not understand neither problem, so I could not show any work. Please help.


The first problem is called a mixture problem. If you go to the Quandaries and Queries page on Math Central and use the Quick Search to search for the word mixture you will find a number of problems of this type and their solutions.

For problem 2 he height of each tree is the initial height plus the number of years times its growth rate.

So if Y = the number of years, then the hemlock's height is 14 + 4Y. What is the spruce tree's height?

You know from the question that at some point, they are the same height, so these two expressions are equal.

Solve for Y.

Stephen La Rocque and Harley Weston

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