+27 A store sold a total of 125 car stereo systems and speakers in one week. The stereo systems sold for $104.95 and the speakers sold for $18.95. The sales from these two items totaled $6926.75. How many of each item were sold?
A store sold a total of 125 car stereo systems and speakers in one week. The stereo systems sold for $104.95 and the speakers sold for $18.95. The sales from these two items totaled $6926.75. How many of each item were sold?
Let stereos=s
Let speakers=k
s+k =125
104.95s + 18.95k=6926.75
Solve the following system:
{k+s = 125
18.95 k+104.95 s = 6926.75
In the first equation, look to solve for s:
{k+s = 125
18.95 k+104.95 s = 6926.75
Subtract k from both sides:
{s = 125-k
18.95 k+104.95 s = 6926.75
Substitute s = 125-k into the second equation:
{s = 125-k
104.95 (125-k)+18.95 k = 6926.75
104.95 (125-k)+18.95 k = 18.95 k+(13118.8-104.95 k) = 13118.8-86. k:
{s = 125-k
13118.8-86. k = 6926.75
In the second equation, look to solve for k:
{s = 125-k
13118.8-86. k = 6926.75
13118.8-86. k = 52475/4-86 k and 6926.75 = 27707/4:
52475/4-86 k = 27707/4
Subtract 52475/4 from both sides:
{s = 125-k
-86 k = -6192
Divide both sides by -86:
{s = 125-k
k = 72
Substitute k = 72 into the first equation:
{s = 53
k = 72
Collect results in alphabetical order:
Answer: | k = 72 and s=53
