Question

Jessica lived in Spain and Colombia for a total of 18 months in order to learn Spanish.She learned an average of 160 words per month when she lived in Spain, and an average of 200 per month when she lived in Colombia. In total, she heard 3200 new words. How long did Jessica live in Spain, and how long did she live in Colombia?

Answer 1

Answer:

Jessica lived 10 months in Spain and 8 months in Colombia.

Step-by-step explanation:

Let x be the months Jessica spent in Spain, and y the months she spent in Colombia:

   1. x + y = 18

Using the information of words per month learned in each country, we can also write the equation:

    2. 160 * x + 200 * y = 3200

So now we have a system of two equations and two unknowns.

First we express y in terms of x, in the first equation:

• x + y = 18

• y = 18 - x

We replace y in the second equation:

• 160 * x + 200 * (18 - x) = 3200

And solve for x:

• 160x + 3600 - 200x = 3200

• -40 x = -400

• x = 10

Finally we use that value of x in the first equation and solve for y:

• 10 + y = 18

• y = 8

Jessica lived 10 months in Spain and 8 months in Colombia.