Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# Pls help with this math question ?

Linda received twice as much profit on her investment as Ella did. Kris received \$200 more than Linda. If the total profit was \$1700, how much did KRIS receive?

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• > Linda received twice as much profit on her investment as Ella did.

TRANSLATION. L = 2E...............

> Kris received \$200 more than Linda.

TRANSLATION. K = L+200.........

> If the total profit was \$1700,

TRANSLATION. E +L + K = 1700.........

>  how much did KRIS receive?

TRANSLATION. Solve for K

// You have 3 equations. Since we're solving for K,

// get L and E in terms of K.

// Rewrite  solving for L

K = L+200.........

L = K -200.........[2a]

// Use [2a] to rewrite E in terms of K

L = 2E..............

E = L/2

E (K-200)/2.......[1a]

// Now use [1a] and [2a] to rewrite  in terms of K

E +L + K = 1700.........

(K-200)

---------- + (K-200) + K = 1700

...2

// Solve for K

(K-200)  + 2(K-200) + 2K = 2(1700)

K - 200 + 2K - 400 + 2K = 3400

5K - 600 = 3400

5K = 4000

K = 800...................ANS

• L = 2E

K = L+ 200

E + L + K =1700

• Let l = Linda's profit

Let e = Ella's profit

Let k = Kris' profit

l = 2e

Kris received \$200 more than Linda:

k = 200 + l

The total profit was \$1,700:

l + e + k = 1700

We have a system of two equations and two unknowns.  Let's start with substituting the expression (200 + l) for "k" in the last equation, then simplify:

l + e + k = 1700

l + e + 200 + l = 1700

2l + e = 1500

Now substitute the expression (2e) in for "l" and simplify, solve for e:

2(2e) + e = 1500

4e + e = 1500

5e = 1500

e = 300

Now that we have "e", we can work back to solve for "l" and "k":

l = 2e

l = 2(300)

l = 600

k = 200 + l

k = 200 + 600

k = \$800 is Kris' profit