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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?

 Sep 14, 2021
 #1
avatar+35058 
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

 Sep 17, 2021
 #2
avatar+12396 
+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.

laugh  !

 Sep 17, 2021
 #3
avatar+282 
+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! smiley

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

 Sep 17, 2021

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