Christine went shopping and bought each of her seven nephews a gift, either a video costing $14.95 or a CD costing $16.88. She spent $112.37 on gifts. How many videos and how many CDs did she buy?
+495 3(14.95) * 4(16.88) = 112.37 so Christine bought 3 videos and 4 CDs.
I divided 112.37 by 7 and the answe was closer to 16.88 so I concluded more CDs were bought than videos. And I was right.
Not very mathematical, but it got the job done :)
Let the number of videos be=x
Let the numbet of CD's be=y, then we have:
x + y=7
14.95x + 16.88y=112.37
Solve the following system:
{14.95 x+16.88 y = 112.37
x+y = 7
In the second equation, look to solve for y:
{14.95 x+16.88 y = 112.37
x+y = 7
Subtract x from both sides:
{14.95 x+16.88 y = 112.37
y = 7-x
Substitute y = 7-x into the first equation:
{16.88 (7-x)+14.95 x = 112.37
y = 7-x
16.88 (7-x)+14.95 x = 14.95 x+(118.16-16.88 x) = 118.16-1.93 x:
{118.16-1.93 x = 112.37
y = 7-x
In the first equation, look to solve for x:
{118.16-1.93 x = 112.37
y = 7-x
118.16-1.93 x = 2954/25-(193 x)/100 and 112.37 = 11237/100:
2954/25-(193 x)/100 = 11237/100
Subtract 2954/25 from both sides:
{-(193 x)/100 = -579/100
y = 7-x
Multiply both sides by -100/193:
{x = 3
y = 7-x
Substitute x = 3 into the second equation:
Answer: |
| {x = 3
y = 4
