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Question

Nora bought 100 shares of a technology stock and 200 shares of a mutual fund for $3800. Her sister, Erin bought 300 shares of the technology stock and 50 shares of the same mutual fund for $5350. Find the cost per share of the technology stock, and the cost per share of the mutual fund.

Answer 1

Let "t" be the cost/share of the technology stock and let "m" the cost/share of the mutual fund:

Then "100 shares of a technology stock and 200 shares of a mutual fund for $3800" means:

100t + 200m = 3800 or t + 2m = 38 meaning that t = 38 - 2m

And "300 shares of the technology stock and 50 shares for $5350" means:

300t + 50m = 5350 or 6t + m = 107

If we plug in "38 - 2m" for "t" (because t = 38 - 2m) then:

6(38 - 2m) + m = 107

228 - 12m + m = 107

-11m = -121

m = 11

Then, using t = 38 - 2m and plugging in m = 11 we get:

t = 38 - 2(11)

t = 38 - 22

t = 16

So the technology stock costs $16/share and the mutual fund costs $11/share

Answer 2