Question

1. A sum of money is shared among three people in the ratio of 15 : 18 : 7. Find the total sum and the
largest share, given that the smallest share is
(a) $84.
(b) $133,
(c) $301.
(d) $3990.​

Answer 1

(a) Total sum = $480 , Largest share = $216.

(b) Total sum = $760 , Largest share = $342.

(c) Total sum = $1720 , Largest share = $774.

(d) Total sum = $22800 , Largest share = $10260.

Step-by-step explanation:

We are given that a sum of money is shared among three people in the ratio of 15 : 18 : 7.

Let the total sum of money in each case be x.

The sum of all three numbers is =  15 + 18 + 7 = 40

(a) We are given that the smallest share is $84.

From the ratio above it is clear that the smallest ratio is $\frac{7}{40}$ .

This means the smallest share will be calculated as;

          $\frac{7}{40} \times x$  =  Amount of smallest share

          $\frac{7}{40} \times x$  =  $84

             $x=\frac{84 \times 40}{7}$  =  $480

SO, the total sum of money in this case is $480.

Now, the largest share is calculated as  =  $\frac{18}{40} \times \text {Total sum of money}$  

                                                                  =  $\frac{18}{40}\times 480$  =  $216

(b) We are given that the smallest share is $133.

From the ratio above it is clear that the smallest ratio is $\frac{7}{40}$ .

This means the smallest share will be calculated as;

          $\frac{7}{40} \times x$  =  Amount of smallest share

          $\frac{7}{40} \times x$  =  $133

             $x=\frac{133 \times 40}{7}$  =  $760

SO, the total sum of money in this case is $760.

Now, the largest share is calculated as  =  $\frac{18}{40} \times \text {Total sum of money}$  

                                                                  =  $\frac{18}{40}\times 760$  =  $342.

(c) We are given that the smallest share is $301.

From the ratio above it is clear that the smallest ratio is $\frac{7}{40}$ .

This means the smallest share will be calculated as;

          $\frac{7}{40} \times x$  =  Amount of smallest share

          $\frac{7}{40} \times x$  =  $301

             $x=\frac{301 \times 40}{7}$  =  $1720

SO, the total sum of money in this case is $1720.

Now, the largest share is calculated as  =  $\frac{18}{40} \times \text {Total sum of money}$  

                                                                  =  $\frac{18}{40}\times 1720$ =  $774.

(d) We are given that the smallest share is $3990.

From the ratio above it is clear that the smallest ratio is $\frac{7}{40}$ .

This means the smallest share will be calculated as;

          $\frac{7}{40} \times x$  =  Amount of smallest share

          $\frac{7}{40} \times x$  =  $3990

             $x=\frac{3990 \times 40}{7}$  =  $22800

SO, the total sum of money in this case is $22800.

Now, the largest share is calculated as  =  $\frac{18}{40} \times \text {Total sum of money}$  

                                                                  =  $\frac{18}{40}\times 22800$  =  $10260.

Answer 2

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let the money divided be 15x,18x,7x

smallest share is 84

→ 7x = 84

→ x=84/7

→ x=12

Now, 15(12)+18(12)+7(12)

→ 180+216+84

→ 480