A girl has exactly enough money to buy 3 sweaters and 2 skirts, or to buy 3 skirts and no sweaters. How many sweaters can she buy is she buys only one skirt
number of sweaters ---- x
number of skirts ------- y
3x + 2y = 3y
3x = y or x = y/3
so she has 3y to spend
if she buys 1 skirt, or she spends y, that leaves her with 2y
but y = 3x, so 2y = 6x = 6 sweaters
check:
suppose she has $90
so she can buy 3 skirts, each skirt would cost $30
but 3 sweaters + 2 skirts cost $90
3x + 60 = 90
3x = 30
x = 10
each sweater would cost $10.
so if she buys only 1 skirt, she would have
90-30 or $60 left, for which she could buy 6 sweaters, as shown above.
To solve this problem, we need to determine the cost of a sweater and a skirt relative to each other.
Let's assume that the cost of a sweater is S and the cost of a skirt is K.
We are given that she has enough money to buy 3 sweaters and 2 skirts, or 3 skirts and no sweaters.
If she buys 3 sweaters and 2 skirts, the total cost would be 3S + 2K.
Similarly, if she buys 3 skirts and no sweaters, the total cost would be 3K.
Since she has exactly enough money for either of these options, we can equate the total costs and solve for S in terms of K:
3S + 2K = 3K
Subtracting 2K from both sides gives:
3S = K
Now, we want to find out how many sweaters she can buy if she buys only one skirt. This means that the total cost would be S + K.
Substituting K = 3S from the equation above, we get:
S + 3S = 4S
Hence, she can buy 4 sweaters if she buys only one skirt.