Step-by-step explanation:
most of the solution is already written there.
in words :
you define 2 variables for the 2 unknown quantities.
per definition we pick
M = number of medium packs
L = number of large packs
in order to solve a system of 2 variables we need 2 different equations about these 2 variables (for 3 variables we need 3 equations and so forth).
she bought 10 packs.
that much we know. and we know how much she paid for these 10 packs in total.
and we know the individual prices for a single pack of medium and of large size.
so,
M + L = 10
we don't know how many of each, but the total number of packs is 10. so, that's what we are writing down, and it becomes our first equation to solve the 2 variables.
and combining our knowledge about individual prices and the total cost we say
1.80M + 2.40L = 21.60
in other words, we still don't know how many of each size she bought, but the sum of the unknowns "weighted" by their individual prices is known in the form of total cost.
and this is then our second equation.
to summarize these equations again :
M + L = 10
1.80M + 2.40L = 21.60
the first equation is the easiest to transform, and we use it to express one variable by the other (apply the same change to both sides, like here subtracting L from both sides) :
M = 10 - L
this identity we can now use in the second equation :
1.80×(10-L) + 2.40L = 21.60
you know, when you multiply 2 expressions, you need to multiply every term of one expression with every term of the other expression. so, we get
1.80×10 - 1.80L + 2.40L = 21.60
18 - 1.80L + 2.40L = 21.60
when you add 2 terms of the same variable, you can simply add the factors of the variable. so, we get
18 + 0.60L = 21.60
when transforming an equation, it is important to always apply the same changes on both sides. so, here, we subtract 18 from both sides :
0.60L = 3.60
now dividing both sides by 0.60 :
L = 6
and from
M = 10 - L
we get
M = 10 - 6 = 4
so, she bought 4 medium packs and 6 large packs.
