Help with 2 linear equation questions

Question

Question 1. A grant of $12,000 is said to be divided into 3 scholarships. How much is given to each scholarship if the second is double the first and the third is $1700 more than the second?


Question 2. A man had $185 in five and ten dollar bills. How many of each did he have if he had 7 fives more than tens?

Answer 1

1//   let x = amt of first, so 2nd is 2x & third = (1700 + 2x); total =

12,000 = (1700 + 2x) + 2x + x.  You take it from there!

 

2// let x = # of $10 bills...7 fives more than ten means # of fives = x + 7;

total $185 = x + (x+7).  You take it from there!

 

It would be very worthwhile to spend time studying the way that each of these word problems was set up.  So often, the work done should begin with "Let x ..."

Answer 2

1). Call the first grant x

     2nd grant = 2x

     3rd grant = 2x + 1700

     Total grant sum = 12000

 

x + 2x + 2x + 1700 = 12000

5x + 1700 = 12000

5x = 12000 - 1700

5x = 10300

x = 10300/5

x = $2060

2x = $4120

2x + 1700 = $5820

 

2). let x = # $5 bills

     let y = # $10 bills

 

y = x-7.    he had 7 more fives than tens

5x + 10y = 185  Total money is$185

 

Put x-7 in place of y in 2nd equation to solve

for the number of $5 bills.

 

5x + 10(x-7) = 185

5x+10x-70=185

15x = 185+70

15x = 255

x = 255/15

x= 17

 

He had 17 fives

 

y = x-7 = 17-7 =10

 

He had 10 tens