SAT Question 431c3038: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice D is correct. Since a $160$-pound adult uses $200$ calories for every $30$ minutes of hiking, then the same adult uses $200h$ calories after hiking for $h$ $30$-minute periods. Similarly, the same adult uses $150b$ calories after bicycling for $b$ $30$-minute periods. Therefore, the equation $200h+150b=1,900$ represents the situation where a $160$-pound adult uses a total of $1,900$ calories from hiking for $h$ $30$-minute periods and bicycling for $b$ $30$-minute periods. It's given that the adult completes $1$ hour, or $2$ $30$-minute periods, of bicycling. Substituting $2$ for $b$ in the equation $200h+150b=1,900$ yields $200h+150\times 2=1,900$, or $200h+300=1,900$. Subtracting $300$ from both sides of this equation yields $200h=1,600$. Dividing both sides by $200$ yields $h=8$. Since $h$ represents the number of $30$-minute periods spent hiking and there are $2$ $30$-minute periods in every hour, it follows that the adult will need to hike for $\frac{8}{2}$, or $4$ hours to use a total of $1,900$ calories from bicycling and hiking.