The ratio of number of $5 notes to the number of $10 notes that Ryan has was 4:3. After Ryan spent $140 worth of 5$ notes and 2/5 of $10 notes, the ratio became 2:3. What was the value of the $5 notes Ryan had at first?

Question

The ratio of number of $5 notes to the number of $10 notes that Ryan has was 4:3. After Ryan spent $140 worth of 5$ notes and 2/5 of $10 notes, the ratio became 2:3. What was the value of the $5 notes Ryan had at first?

Answer 1

At the start:

number of fives ---- 4x
number of tens ----- 3x

$140 in fives = 28 notes
so he has 4x-28 of the fives left over

he also spent 2/5 of his tens, so he has 3/5 of the tens left
or he has 3/5(3x) or 9x/5 tens left over

(4x-28)/( (9x/5)) = 2/3
12x - 84 = 18x/5
60x - 420 = 18x
42x = 420
x = 10

So originally he had 40 fives, and
30 tens

check:
after spending 28 of his 40 fives he has 12 fives left
after spending 2/5 of his 30 tens, he has 3/5 of 30, or
18 tens left.
Ratio of 12 : 18 = 2: 3
My answer is correct

Answer 2

Thank you so much Reiny!!!

Help a lot! :)

Answer 3

To solve this problem, let's assign variables to the unknown quantities. Let's denote the number of $5 notes Ryan had initially as 'x' and the number of $10 notes as 'y.'

According to the problem, the ratio of the number of $5 notes to the number of $10 notes that Ryan had initially was 4:3. Therefore, we can say that:

x/y = 4/3

Next, the problem states that Ryan spent $140 worth of $5 notes and 2/5 of the $10 notes. Let's calculate the number of $10 notes Ryan spent:

2/5 * y

Now, let's express the new ratio of $5 notes to $10 notes after the expenditure:

(x - 140) / (y - (2/5 * y)) = 2/3

Simplifying the above equation:

(x - 140) / (3/5 * y) = 2/3

Now, we can solve the system of equations formed by the two ratios to determine the values of 'x' and 'y.' Let's start by isolating 'x' in the first equation:

x = (4/3) * y

Substituting this value of 'x' in the second equation:

((4/3) * y - 140) / (3/5 * y) = 2/3

Next, let's solve for 'y':

(4/3 * y - 140) = (2/3 * 3/5 * y)

Multiplying both sides by (3/5):

(4/3 * y - 140) * (3/5) = 2/3*y

Simplifying:

(12/15*y - 840/5) = (2/3) * y

Combining like terms:

(12/15 - 2/3) * y = 840/5

(8/15) * y = 840/5

To isolate 'y,' multiply both sides by (15/8):

y = (840/5) * (15/8)

Simplifying:

y = 252

Now that we have found the value of 'y,' we can substitute it back into the equation for 'x':

x = (4/3) * 252

Simplifying:

x = 336

Therefore, the value of the $5 notes Ryan had initially was $336.