Lennox owns a big apple orchard. She ships her apples to various markets using a fleet of trucks. Every week, each truck goes on 3 trips, and for each trip Lennox gets 300 dollars. On a single trip, a truck delivers 50 packs, and each pack contains 12 kilograms of apples. Overall, Lennox sells 4500 dollars worth of apples in a week. How many trucks are in Lennox's fleet?
Answers
Answer:
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Answer:
5 trucks
Step-by-step explanation:
Let's say there are x trucks in Lennox's fleet. We are given that Lennox makes a total of 4500 dollars each week. How can we relate these two quantities with an equation?
1. x trucks ⋅ y dollars/truck = 4500 dollars
So in order to find the number of trucks x, we need to figure out the value of y, which is the rate of dollars per truck.
---
Notice what other information we are given:
-
50, start fraction, start text, p, a, c, k, s, end text, divided by, start text, t, r, i, p, end text, end fraction
12\,\dfrac{\text{kilograms}}{\text{pack}}12
pack
kilograms
12, start fraction, start text, k, i, l, o, g, r, a, m, s, end text, divided by, start text, p, a, c, k, end text, end fraction
Which of these quantities can help us calculate a rate whose units are \dfrac{\text{dollars}}{\text{truck}}
truck
dollars
start fraction, start text, d, o, l, l, a, r, s, end text, divided by, start text, t, r, u, c, k, end text, end fraction?
Hint #3
We can combine the following quantities:
\begin{aligned} 3\,\dfrac{\cancel\text{trips}}{\text{truck}}\cdot 300\,\dfrac{\text{dollars}}{\cancel\text{trip}}=900\,\dfrac{\text{dollars}}{\text{truck}} \end{aligned}
3
truck
trips
⋅300
trip
dollars
=900
truck
dollars
Now we can plug that in the original equation:
\begin{aligned} x\,\text{trucks}\cdot 900\,\dfrac{\text{dollars}}{\text{truck}}&=4500\,\text{dollars} \\\\ x\,\text{trucks}&=\dfrac{4500}{900}\,\cancel\text{dollars}\cdot\dfrac{\text{trucks}}{\cancel\text{dollar}} \\\\ x\,\text{trucks}&=5\,\text{trucks}\end{aligned}
xtrucks⋅900
truck
dollars
xtrucks
xtrucks
=4500dollars
=
900
4500
dollars
⋅
dollar
trucks
=5trucks
In conclusion, Lennox's fleet has 5 trucks.