Question

Linear Inequalities: Sally intends to give 12 good friends toys. Her friends can either have a teddy bear or a toy car. A teddy bear cost $1.50 while a toy car cost $1.20. If she only has $16 to spend on the gifts, what is the max n.o of teddy bear her friend can have. Solve in linear inequalities.:D
Let x be the max n.o of teddy bear
This is what i have done so far
1.50x-1.2(12-x)<16
2.7x<30.4

Answer 1

Let x be the no of teddy bear. Since her friend can either have a teddy bear or a car. The number of car she buys = 12-x

For the total price of buying cars, it is = 1.2 (12-x)
For the total price of buying teddy bear, it is = 1.5x

So the total money she spends on the gifts
= total price of buying cars + total price of buying teddy bear
= 1.2(12-x) +1.5x

Note that she has only 16 dollars, so the amount she spends cannot exceed $16
So, the total amount spent should be less than or equal to 16, and you can write the inequality like this:
total price of buying cars + total price of buying teddy bear ≦ 16
1.2(12-x) +1.5x ≦ 16
14.4 -1.2x +1.5x ≦ 16
Can you solve it from here?
Note that once you find that it is a fraction ( or decimal) , say 5.23, that maximum no of teddy bear you can buy is the largest integer satisfying the inequality, that is 5

(5.23 is not the answer, it's just an example)
Can you work it out now?

Answer 2

b + c = 12 toys
1.5b + 1.2 c <= $16

-> 1.2b + 1.2c = 14.4
=> b = 1.6 / .3 = 5.3 Max is 5 bears