SOLUTION: The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find the cost of each orange Sam invested a total of $10,000, part at 8% and the rest at 3%.

Question 214685: The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find the cost of each orange
Sam invested a total of $10,000, part at 8% and the rest at 3%. How much was invested at 8% if he earned a total of $600 in one year? (Use the formula , Interest = principal * time * rate)
In an office there was a small cash box. One day Jane took half of the money plus $1 more. Then Mike took half of the remaining money plus $1 more. Rob then took the remaining $6. How many dollars were originally in the box?
The sum of two numbers is 8 less than twice the first number. Their difference is 4 less than twice the second number. What is the larger number?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find the cost of each orange
---
Equations:
12r + 7a = 536 cents
8r + 5a = 368 cents
---------------------------
Get rid of the "a's":
Multiply 1st Eq. by 5 and 2nd Eq. by 7 to get:
---
60r + 35a = 5*536
56r + 35a = 7*368
--------------------------
Subtract the 2nd from the 1st and solve for "r":
4r = 104
r = 26 cents (cost of one orange)
===========================
Sam invested a total of $10,000, part at 8% and the rest at 3%. How much was invested at 8% if he earned a total of $600 in one year? (Use the formula , Interest = principal * time * rate)
---
Interest + interest = interest
0.08x + 0.03(10000-x) = 600
Multiply thru by 100 to get:
8x + 30000 - 3x = 60000
5x = 30000
x = 6000 (amt invested at 8%)
4000 (amt invested at 3%)
==============================
In an office there was a small cash box. One day Jane took half of the money plus $1 more. Then Mike took half of the remaining money plus $1 more. Rob then took the remaining $6. How many dollars were originally in the box?
---
Start : x
After Jane: x -(1/2)x-1 = (1/2)x -1
-----------------------------------
After Mike: [(1/2)x-1] - [(1/2)x-1]/2 -1 = (1/2)[(1/2)x-1]-1
= (1/4)x - (3/2)
-----------------------------------
Equation:
(1/4)x - (3/2) = 6
(1/4)x = 7.5
x = 30
------------------------
Checking:
30 -(15+1) = 14
14-(7+1) = 6
---------------------
OK
Original amount = $30
=========================
The sum of two numbers is 8 less than twice the first number. Their difference is 4 less than twice the second number. What is the larger number?
-------------------------
Equations:
a + b = 2a-8
a - b = 2b-4
------------------
Rearrange:
a = b + 8
a = 3b-4
-----------------
Substitute to get:
b+8 = 3b-4
2b = 12
b = 6
---
Substitute into a = b+8 to get:
a = 14
================================================
Cheers,
Stan H.
RELATED QUESTIONS
The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find (answered by Maths68)

The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find (answered by Cromlix)

The cost of 12 oranges and 7 apples is $5.36. 8 oranges and 5 apples cost $3.68. what is... (answered by stanbon,Mathtut,josmiceli)

Linear System Word Problems Please help me figure this out. The cost of 12 oranges... (answered by ankor@dixie-net.com)

The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find (answered by oberobic)

The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68.... (answered by scott8148)

The cost of 5 apples and 3 oranges is $2.18. 3 apples and 1 orange cost $1.02. Find the... (answered by josgarithmetic)

If 5 apples and 4 oranges cost $3.40 while 7 apples and 6 oranges cost $4.90.Find the... (answered by prabhjyot)

2 oranges and 5 apples cost $2.50 3 oranges and 4 apples cost $2.70 find the cost of... (answered by Paul)

Four oranges and five apples cost $2.00. Three oranges and four apples cost $1.56. Find... (answered by mananth)