SOLUTION: Hi when belinda purchased 6kg of rice she was 6 dollars short.when she purchased 8kg of the same type of rice she was 14 dollars short.how much money did she have. Thanks

Question 1103357: Hi
when belinda purchased 6kg of rice she was 6 dollars short.when she purchased 8kg of the same type of rice she was 14 dollars short.how much money did she have.
Thanks

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
she purchased 6 kg of rice and was 6 dollars short.

when she purchased 8 kg of the same rice, she was 14 dollars short.

if she was short dollars, then the cost of the rice must have been more dollars than she had.

let the amount of money that she had = x.

the cost of 6 kg of rice must have been x + 6.

the cost of 8 kg of rice must have been x + 14.

the difference was 2 kg of rice for 8 dollars.

the cost per kg of rice must have been 4 dollars each.

6 * 4 = 24.
she was 6 dollars short.
she must have had 18 dollars.

8 * 4 = 32
she was 14 dollars short.
she must have had 18 dollars.

it appears that she must have had 18 dollars.

algebraically, you might solve this as follows:

let c = the cost per kg of the rice.
let x = the total cost.

your first equation would be 6 * c = x + 6
your second equation would be 8 * c = x + 14

subtract x from both sides of each equation to get:

6c - x = 6
8c - x = 14

these are the two equations you want to solve simultaneously.

subtract the first equation from the second to get:

2c = 8

solve for x to get c = 4.

when c = 4, both equations becomes:

6 * 4 - x = 6
8 * 4 - x = 14

these simplify to:

24 - x = 6
32 - x = 14

add x to both sides of each equation and subtract 6 from both sides of the first eqution and subtract 14 from both sides of the second equation to get:

24 - 6 = x
32 - 14 = x

solve for x in each equation to get:

x = 18
x = 18

your solution is that she must have had 18 dollars.

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