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 words per month when she lived in colombia. In total, she learned a total of 3200 new words.

Answer 1

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

Explanation:

Let x be the number of months Jessica lived in Spain, then she lived 18 - x months in Colombia.

She learned an average of 160 words per month when she lived in Spain, so she learned 160x words in Spain.

She learned an average of 200 words per month when she lived in Colombia, so she learned 200(18-x) words in Colombia.

In total, she learned a total of 3,200 new words, thus

`160x+200(18-x)=3,200\\ \\160x+3,600-200x=3,200\\ \\160x-200x=3,200-3,600\\ \\-40x=-400\\ \\x=10`

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