Lauren saved $84 more than Fiona. 1/5 of Laurens savings was the same as 3/8 of Fionas savings. How much did Lauren and Fiona save altogether?

Question

Lauren saved $84 more than Fiona.  1/5 of Lauren was the same as 3/8 of Fiona's savings.  How much did Lauren and Fiona save altogether?

Answer 1

Hi Melissa;

 

FIRST EQUATION...L=$84+F

 

(1/5)L=(3/8)F

Let's isolate L by multiplying both sides by 5...

SECOND EQUATION...L=(15/8)F

 

Let's subtract the second equation from the first...

0=$84+[F-(15/8)]

0=$84+[(8/8)F-(15/8)F]

0=$84+[(-7/8)F]

Let's subtract $84 from both sides...

-$84=(-7/8)F

Let's multiply both sides by (-8/7)...

$96=F

 

FIRST EQUATION...

L=$84+F

L=$84+$96

L=$180

 

SECOND EQUATION...

L=(15/8)F

$180=(15/8)($96)

$180=$180

 

TOTAL AMOUNT SAVED...$96+$180=$276

 

Answer 2

We have to first find out how much they saved individually, and then add the two amounts together.

 

Let  x = amount Fiona saved

 

Let  ( x + 84) = amount that Lauren saved

 

1/5 (x + 84) = 3/8 x      ( I/5 of Lauren's savings equals 3/8 of Fiona's)

 

To clear the fractions, multiply both sides of the equation by the LCD of 40.

 

8(x + 84) = 15x            

8x + 672 =  15x

       672 = 7x

         96 = x

 

Therefore, Fiona saved $96 and Lauren saved $180

 

Together, they saved $96 + $180 for a total of $276.

 

 

 

Answer 3

L= Lauren's savings

F = Fiona's savings 

Lauren saved $84 more than Fiona. So...... L = 84 + F

1/5 of Lauren's savings was the same as 3/8 of Fiona's. So...... (1/5)L = (3/8)F

Now you have a system of equations. the first equation is already solved for L, so you can plug 84+F in for L in the section equation to get..... (1/5)(84+F)=(3/8)F Then solve for F and plug it in to one of the original equations to get L. Then add L and F together to get the total amount they saved. Good Luck!

Answer 4

eq_1: L = F + 84

eq_2: 1/5 L = 3/8 F

 

Multiply eq_2 by 40:

eq_3: 8 L = 15 F

Substitute eq_1 into eq_3:

8(F + 84) = 15 F

8 F + 8*84 = 15 F

7 F = 8*84

F = 8*84/7 = 8*12 = 96

Substitute into eq_1:

L = 96 + 84 = 180

Add them up:

F + L = 96 + 180 = $276