Question

Mr. Atinga shared his cattle among his three children Lordia,Anita,and Richmond. He gave 3/5 of cattles to Anita and shared the remaining between Lordia and Richmond in the ratio 2:3 respectively. In all 80 cattle were shared between Lordia and Richmond. How many cattle were shared among the three children How many cattle did Anita receive than Richmond

Answer 1

a). The total number of cattle shared among the three children=200

b). Anita's share=120 cattle

Lordia's share=32 cattle

Richmond's share=48 cattle

Explanation:

a)

Step 1

Determine fraction shared between Lordia and Richmond as follows;

Lordia:Richmond=2:3

Let the total cattle be x

Lordia's fraction=2/(2+3)=2/5 of x=(2/5)x

Lordia's fraction=(2/5)x

Richmond's fraction=3/(2+3)=3/5 of x=(3/5) x

but;

x=80 cattle

replacing;

Total number of cattle Lordia got=(2/5)×80=32 cattle

Total number of cattle Richmond got=(3/5)×80=48 cattle

Step 2

Express the total cattle Mr. Atinga had initially as follows;

Let the initial number of cattle be y

The fraction remainder given to Lordia and Richmond=Initial number-fraction of the totat given to Anita

where;

Initial number=y

fraction of the total given to Anita=3/5 y

replacing;

The fraction remainder given to Lordia and Richmond=y-3/5 y=2/5 y

but;

2/5 y=80

y=80×5/2=

y=200

The total number of cattle shared among the three children=200

b).

Anita's share=(3/5)×200=120 cattle

Lordia's share=(2/5)×80=32 cattle

Richmond's share=(3/5)×80=48 cattle