Henry spent 3/8 of his money on a badminton racket. He spent 1/8 of his money on a watch. The badminton racket cost $14 more than the watch. How much money did Henry spend on the two items altogether?

Guest Sep 14, 2021

#1**0 **

3/8 ths x on racket - 1/8x on watch = 14

3/8 x - 1/8 x = 14

2/8 x = 14

x = 14 * 8/2 = 14 * 4 = 56 dollars initially

(3/8 + 1/4) 56 = 35 dollars total

ElectricPavlov Sep 17, 2021

#2**+1 **

How much money did Henry spend on the two items altogether?

**Hello Guest!**

Henry owns x.

\(\color{blue}\frac{x}{8}+$14=\frac{3x}{8}\\ \frac{3x-x}{8}=$14\\ 2x=$112\)

\(x=$56\)

\((\frac{1}{8}+\frac{3}{8})\cdot $56=\color{blue}$28\)

$28 did Henry spend on the two items altogether.

!

asinus Sep 17, 2021

#3**+3 **

Straightforward. First, assign variables to the unknown values:

Let H = Henry’s money

Let B = Badminton Racket

Let W = Watch

We are given:

B = 3/8 H

W = 1/8 H

B = W + $14

So:

Substitute B and W:

3/8 H = 1/8 H + $14 [Cost of Badminton racket = $14 more than cost of watch]

Solving:

3/8 H - 1/8 H = $14

(3/8–1/8) H = $14

2/8 H = $14

1/4 H= $14

H = 4 * $14 = $56 [Henry’s total money]

B = 3/8 * $56 = $21 [Cost of badminton racket]

W = 1/8 *$56 = $7 [Cost of watch]

Check:

B = W + $14

$21 =? $7 + $14

Yes!

Henry spent B+W on his items altogether, which is $21+$7 = $28.

Another way of expressing it is:

2/8 H = $14

1/8 H = $7

B+W = 3/8 H + 1/8 H = (3+1)/8 H = 4/8 H = 1/2 H.

H = $56

B+W = 1/2 H = $28

apsiganocj Sep 17, 2021