# Thread: Systems of Two Equations... Word Problems

1. ## Systems of Two Equations... Word Problems

I've been struggling on how to set up these two word problems. The first one is a mixture problem while the second is about motion; I believe.

1) In order for coffee to be labeled "Kona Blend," it must contain at least 30% Kona beans. Bean Town Roasters has 40 lb of Mexican coffee. How much Kona coffee must they add if they wish to market it as Kona Blend?

2) Natalie jogs and walks to school each day. She averages 4 km/h walking and 8 km/h jogging. From home to school is 6 km and Natalie makes the trip in 1 hr. How far does she jog in a trip?

2. Originally Posted by CODEONE
I've been struggling on how to set up these two word problems. The first one is a mixture problem while the second is about motion; I believe.

1) In order for coffee to be labeled "Kona Blend," it must contain at least 30% Kona beans. Bean Town Roasters has 40 lb of Mexican coffee. How much Kona coffee must they add if they wish to market it as Kona Blend?
since they said "at least", technically we want inequalities here, but i'll use equations.

Let $x$ be the amount, in pounds, of Kona beans we add to the coffee to make it a Kona Blend. then at the end, we will have $40 + x$ pounds of Kona Blend. now we want the amount of Kona Beans to be 30% of the mixture of the Kona Blend, thus we want:

$x = 0.3(40 + x)$

now solve for $x$

3. Originally Posted by CODEONE
2) Natalie jogs and walks to school each day. She averages 4 km/h walking and 8 km/h jogging. From home to school is 6 km and Natalie makes the trip in 1 hr. How far does she jog in a trip?
we need to know that $\mbox{Speed } = \frac {\mbox{Distance}}{\mbox{Time}} \implies \mbox{Time } = \frac {\mbox{Distance}}{\mbox{Speed}}$

now, let $x$ be the distance she walks
let $y$ be the distance she jogs

since she travels 6 km, we have:

$x + y = 6$ ..................(1)

since she walks at a speed of 4 km/h and jogs at a speed of 8 km/h, the time she spends walking (in light of the formula i gave you above) is: $\frac x4$ and the time she spends jogging is: $\frac y8$. since the total time she travels is one hour, we have:

$\frac x4 + \frac y8 = 1$ ...................(2)

there are your two equations, now solve for $y$ ONLY

4. Thanks for the help, especially with the second one; I don't think I'd ever think of that. Thanks again.

5. Originally Posted by CODEONE
Thanks for the help, especially with the second one; I don't think I'd ever think of that. Thanks again.
you're welcome