In this question, we have two unknowns: p and q. The golden rule for solving for 2 variables is that we need 2 equations (although there are some exceptions. See here:
https://www.beatthegmat.com/to-find-the- ... tml#706713 )
(1) A customer who buys 2 loaves is charged 10 percent less per loaf than a customer who buys a single loaf.
If we were to set this up algebraically, we'd want to find the average of 2 loaves, and compare it to a single loaf:
(p + q)/2 = 0.9p
Here, we have one equation with two variables. We can quickly test values to see if this works for multiple scenarios. We weren't given any integer constraints (they don't have to be WHOLE dollar amounts), so we can test anything that fits.
If p = $1, then q would equal $0.80
If p = $100, then q would equal $80
Ridiculous for prices of bread, obviously! But the point is - one equation was not enough for us to solve. Insufficient.
2) A customer who buys 6 loaves of bread is charged 10 dollars.
Again, set this up algebraically:
p + 5q = 10
We can easily see that there are multiple possibilities that would add up to 10: p=5 and q=1, p=2.50 and q=1.50, etc. Insufficient.
1&2
If we put the statements together, we have two equations with two variables. We can solve for q in the first equation:
(p + q)/2 = 0.9p
p + q = 1.8p
q = 0.8p
Then we can easily plug it into the second equation and solve. Since it's DS - don't actually do the work! You can see that you'll get a value for p, but you don't have to actually figure out what it is.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
