Before the Mars lander could launch, Emek and Luna had to verify its cargo. The lander carried food containers weighing 6 kilograms each and equipment containers weighing 9 kilograms each. The loading display showed 23 containers with a combined mass of 165 kilograms. Emek let f represent the number of food containers and e represent the number of equipment containers. They wrote f + e = 23 and 6f + 9e = 165. Luna multiplied the first equation by 6, giving 6f + 6e = 138. Subtracting this from the mass equation left 3e = 27, so e = 9. Then f = 14. They checked that 14 + 9 = 23 and that 6(14) + 9(9) = 165. Both conditions matched the display. With 14 food containers and 9 equipment containers correctly loaded, Emek and Luna approved the balanced cargo, and the Mars lander was cleared for launch.

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
Compare the coefficient of f in 6f + 9e = 165 with the coefficient of f after multiplying the first equation by 6.
Luna multiplied f + e = 23 by 6 before subtracting it from 6f + 9e = 165. Why was multiplying by 6 a useful choice?
It made both equations have the same constant.It made the coefficients of f equal, so subtracting the equations would eliminate f.It made the coefficients of e equal, so subtracting the equations would eliminate e.It changed the total number of containers from 23 to 6.
Correct. Both equations then contain 6f, so subtraction eliminates f.
Not quite. Look at which variable has matching coefficients after the first equation is multiplied by 6.
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Hint
Write the same type of system as in the story. Multiply the container-count equation by 6 and subtract.
Suppose a new loading display still shows 23 containers, with food containers weighing 6 kilograms each and equipment containers weighing 9 kilograms each, but the total mass is now 174 kilograms. How many equipment containers are there?
Correct. The new cargo would contain 12 equipment containers.
Check the two equations for container count and total mass, then eliminate the food-container variable.
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Hint
A solution to a system must satisfy both the container-count equation and the mass equation.
A student claims that 13 food containers and 10 equipment containers could also match the original loading display because 13 + 10 = 23. What is the best way to check the student's claim?
Accept the claim because any pair totaling 23 satisfies the cargo conditions.Check only whether the number of food containers is greater than the number of equipment containers.Calculate 6(13) + 9(10) and compare the result with the required mass of 165 kilograms.Subtract 10 from 13 and compare the result with 23.
Correct. The proposed numbers satisfy the container count but must also be checked against the total mass.
Not quite. Matching the total number of containers is only one condition; the mass condition must also be satisfied.
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Mars İniş Aracını Yüklemek
TR
ARC_G08_PA_02_STORY_03
Mars İniş Aracını Yüklemek
Loading the Mars Lander
EN
ARC_G08_PA_02_STORY_03
Loading the Mars Lander