# Thread: Simultaneous Linear Equations help.

1. ## Simultaneous Linear Equations help.

Q1
An investor received $1400 per annun from a sum of money, with part of it invested at 10% and the remainder at 7% interest. This investor found that if she interchanged the amounts she had invested she could increase her return by$90 per annun. Calculate the total amount invested.

Q2
A shopkeeper sold his entire stock of shirts and ties in a sale for $10 000. The hirts were priced at 3 for$100 and the ties $20 each. If he had sold only half the shirts and two-thirds of the ties he would have$6000. How many of each did he sell?

Any help would be appreciated. I would also like to know how to figure these out step by steps.

2. Question 1
Let x be the amount of money invested with the 10% interest.
Equation would be $(12)(0.1x) + (1400-x)(12)(0.07) = (1400 - x)(12)(0.1) + 12(0.07x)$
$1.2x + 1176 - 0.84x = 1680 - 1.2x + 0.84x - 90$
$x = 575$
Invested in 10% = $575, invested in 7% -$825

Question 2
Let x be the amount of shirts the shopkeeper owns
Let y be the amount of ties the shopkeeper owns
Hence, $(100)(\frac{x}{3}) + 20y = 10000$
$100x + 60y = 30000$ - eqn 1
$(100)(\frac{x}{6}) + (\frac{2}{3})(20y) = 6000$
$100x + 80y = 36000$ - eqn 2
eqn 2 - eqn 1 = $100x + 80y - 100x - 60y = 36000 - 30000$
$20y = 6000$
$y = 300, from eqn 1, x = 120$

3. You got the answer for Q2, but not Q1. Thanks anyways.