Question 1151877: Jennifer has a large sum of money in hundred dollar bills, fifty dollar bills, ten dollar bills and five dollar bills. She has seven fewer hundreds than fifties and thirty more fives than fifties. She has one more than twice as many tens than fifties.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
It sounds like you're trying to find how many bills there are.
Let,
H = number of hundred dollar bills
F = number of fifty dollar bills
T = number of ten dollar bills
V = number of five dollar bills
Given Facts
- Fact 1: She has seven fewer hundreds than fifties
- Fact 2: She has thirty more fives than fifties.
- Fact 3: She has one more than twice as many tens than fifties.
From fact 1, we can say
H = F-7
call this equation (1)
Fact 2 translates into
V = F+30
call this equation (2)
and fact 3 means
T = 2F+1
basically whatever amount of fifties we have, double it and add 1 to get the amount of tens
call this equation (3)
Based on the variables we set up,
100H = total value of all the hundred dollar bills
50F = total value of all the fifty dollar bills
10T = total value of all the ten dollar bills
5V = total value of all the five dollar bills
Let,
A = total amount of money in dollars
This is equal to the sum of the previous subtotals
A = 100H+50F+10T+5V
Now apply various steps of substitution and simplify.
A = 100H+50F+10T+5V
A = 100(F-7)+50F+10T+5V ... replace H with F-7 (equation (1))
A = 100F-700+50F+10T+5V ... distribute
A = 100F+50F+10T+5V-700
A = 150F+10T+5V-700
A = 150F+10T+5(F+30)-700 ... replace V with F+30 (equation (2))
A = 150F+10T+5F+150-700 ... distribute
A = 150F+5F+10T+150-700
A = 155F+10T-550
A = 155F+10(2F+1)-550 ... replace T with 2F+1 (equation (3))
A = 155F+20F+10-550 ... distribute
A = 175F-540
We have established a direct connection between the number of fifties (F) and the total amount of money in dollars (A).
If we knew the value of F, then can calculate A.
If we knew the value of A, then we could solve for F.
If we knew the value of F, then we could find the other values H, T, and V.
Unfortunately at this point is where we don't have enough information to solve. I would double check with the teacher to make sure you have all of the info needed to solve the problem. I have a feeling the phrasing "Jennifer has a large sum of money" should be more specific as to how much money she has (either the total dollar amount or the total number of bills).
|
|
|
