Question

Ravi has $\$200$ with which to purchase bags and goggles. Each bag costs the same amount of money and each goggles cost the same amount of money. If Ravi spends all his money entirely on bags, he will get 40 bags. If he purchases only goggles, he will get 80 goggles. Which of the following best models the relationship between the number of bags $b$ and the number of goggles, $g$, that Ravi could purchase with his money?

• A. $40b+80g=400$
• B. $80b+40g=200$
• C. $5b+2.5g=200$
• D. $2.5g+5g=200$

Answer 1

The correct option is C $5b+2.5g=200$

Consider the following verbal model :
Cost per bag no. of bags + cost per goggle no. of goggles = total cost
We know that Ravi spends all of his money $\left(\$200\right)$ on bags, he will get 40 bags. Therefore, we can divide 200 by 40 to see that each bag costs $\$5$.
Similarly, $\frac{200}{g}=2.5$ $\$2.5$ for each goggle.
Now we can substitute this information, along with given information into the above verbal model to find the following equation: $5b+2.5g=200$
Correct option is C.