Question

The ratio of the amount of money Kate had to the amount of money Sam had was 5 : 4. After both of them spent $5, the ratio became 10 : 7. How much money did Sam have at first?

Answer 1

Answer:

$ 12

Step-by-step explanation:

Given :-

The ratio of the amount of money Kate had to the amount of money Sam had was 5 : 4.

Both of them spent $5, then ratio became 10 : 7

To find :-

Initial amount of Sam .

Solution :-

Given that

The ratio of the amount of money of Kate and Sam = 5:4

Let they be $ 5X and $ 4X

The amount of Kate = $ 5X

The amount of Sam = $ 4X

Given that

The money spent by both of them = $ 5

The money after spent $ 5 by Kate

= $ (5X-5)

The money after spent $ 5 by Sam

= $ (4X-5)

The ratio of the money after spent $ 5 each by both of them

= (5X-5) : (4X-5)

According to the given problem

The ratio after money spent by both of them = 10:7

Therefore, (5X-5) : (4X-5) = 10:7

We know that

a:b can be written as a/b

Therefore, (5X-5)/(4X-5) = 10/7

On applying cross multiplication then

=> (4X-5)×10 = (5X-5)×7

=> 40X-50 = 35X -35

=> 40X -35X = -35+50

=> 5X = 15

=> X = 15/5

=> X = 3

Therefore, The value of X = $ 3

If X = 3 then 5X = 5(3) = $ 15

If X = 3 then 4X = 4(3) = $ 12

Sam had $ 12 initially.

Answer:-

The money Sam has initially is $ 12

Check :-

We have,

Amount of Kate = $ 15

Amount of Sam = $ 12

Their ratio = 15:12

=> 15/12

=> (5×3)/(4×3)

=> 5/4

=> 5:4

and

If they spend $ 5 each then

The amount of Kate = 15-5 = $ 10

The amount of Sam = 12-5 = $7

Their ratio = 10:7

Verified the given relations in the given problem

Used formulae:-

→ a:b can be written as a/b

Answer 2

Answer:

Given :-

• The ratio of the amount of money Kate had to the amount of money Sam had was 5 : 4 after both of them spent $ 5 , the ratio become 10 : 7 .

To Find

• How much money did Sam have at first.

Solution :-

Let,

➳ The sum of money does Kate had initially get be $5x

➳ The sum of money does Sam had initially get be $4x

✫ They spent $5 :

★ Total money Kate spent :

$\leadsto \sf\bold{\blue{Total\: Money\: Kate\: Spent =\: \ (5x - 5)}}$

★ Total money Sam spent :

$\leadsto \sf\bold{\blue{Total\: Money\: Sam\: Spent =\: \ (4x - 5)}}$

According to the question :

☆ After spent $ 5, the ratio becomes 10 : 7.

So,

$\implies \bf (5x - 5) : (4x - 5) =\: 10 : 7$

$\implies \sf \bigg\{\dfrac{(5x - 5)}{(4x - 5)}\bigg\} =\: \bigg\{\dfrac{10}{7}\bigg\}$

$\implies \sf \dfrac{5x - 5}{4x - 5} =\: \dfrac{10}{7}$

By doing cross multiplication we get,

$\implies \sf 10(4x - 5) =\: 7(5x - 5)$

$\implies \sf 40x - 50 =\: 35x - 35$

$\implies \sf 40x - 35x =\: - 35 + 50$

$\implies \sf 5x =\: 15$

$\implies \sf x =\: \dfrac{15}{5}$

$\implies \sf\bold{\red{x =\: \ 3}}$

Hence, the money get by both is :

✯ The sum of money does Kate had initially get :

$\dashrightarrow \sf Kate\: get =\: \ 5x$

$\dashrightarrow \sf Kate\: get =\: \ 5(3)$

$\dashrightarrow \sf\bold{\red{Kate\: get =\: \ 15}}$

✯ The sum of money does Sam had initially get :

$\dashrightarrow \sf Sam\: get =\: \ 4x$

$\dashrightarrow \sf Sam\: get =\: \ 4(3)$

$\dashrightarrow \sf\bold{\red{Sam\: get =\: \ 12}}$

$\therefore$ The sum of money does Sam had initially get is $12 .