Question

Funds are distributed to five families affected by floods in the ratio 5:12:2:15:29. The total amount that the five families received was $630.

a) The first family received _____
b) The difference between the amount of money the first and last family received was _____
c) A sixth family joins. They receive n amount of money and the average amount of money donated to all six families becomes 140. How much money does the sixth family receive?

Answer 1

Explanation:

• We must first add up the ratios:5+12+2+15+29 = 63, this will be the total ratio the money was shared
• Then we pick out the ratio for each family accordingly:

For the first family, 5 out of the total ratio = 5/63

For the second family, 12 out of the total ratio = 12/63

For the third family, 2 out of the total ratio = 15/63

For the fifth family, 29 out of the total ratio = 29/63

a) The first family = 5/63 of the money, $630

we can therefore say the money they received is

= 5/63 ×630

= $50

b) The last family = fifth family = 29/63 of the money, 630

= 29/63 × 630

= $290

recall that the first family received $50 , the positive difference between the money received by both the first and last family

= $290 - $50

= $240

c) Since another family joins in, the total number of families become 6

• the money the received is n

we can't find the average without knowing what the second, third, and fourth family received out of that money

• we apply the same step

the second family = 12/63 ×630

= $120

the third family = 2/63 × 630

= $20

the fourth family = 15/63 × 630

= $150

• Average generally is = total sum/ frequency or number of occurrences or people

in this case, we were told the average became $140

which means that

sum of money received by the families/ the number of families involved in the sharing = $140

( $50+$120+$20+$150+$290+n)/6 = $140

($630+n)/6= $140

now the plan would be to make n subject of formula

• multiply both sides of the equation by 6, the equation will become

$630+n = $840

take $630 to the other side, it becomes -$630

n = $840-$630

n = $210

therefore the newly added family received $210

I honestly hope I explained it properly...thank you