Question:
Abraham has visited at least 50 countries; he plans to visit five new countries per year (Y) for the next several years. Which inequality and solution shows the amount of years they will take for Abraham to meet his goal.
Answer:
[tex]Countries \geq 50 + 5y[/tex]
[tex]y \leq 29[/tex]
Step-by-step explanation:
Given
[tex]Countries = 50[/tex] ------ at least
[tex]Yearly =5[/tex]
Required
Represent as an inequality
"at least" means [tex]\geq[/tex]
So the countries he has visited can be represented as thus;
[tex]Countries \geq 50[/tex]
If
1 year = 5 countries
y years would be 5y countries
So, in y years; he'd have visited
[tex]Countries \geq 50 + 5y[/tex]
To determine the value of y.
We have that
[tex]Countries = 195[/tex] in the world
Substitute 195 for Countries
[tex]195 \geq 50 + 5y[/tex]
Collect Like Terms
[tex]195 - 50 \geq 5y[/tex]
[tex]145 \geq 5y[/tex]
Divide through by 5
[tex]145/5 \geq y[/tex]
[tex]29 \geq y[/tex]
Reorder
[tex]y \leq 29[/tex]
This means that; he'll visit all countries in at most 29 years' time
