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Divide $312 so that . . . Word Problem

by Connor
(Canberra, Australia)










































Can someone please tell me the formula to work out the following question? I'm stumped. Thanks in advance.

Divide $312 so that:
(a) Doris gets twice what Dennis gets
(b) Dennis gets three times what Doris gets

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May 24, 2012
Divide $312 so that . . .
by: Staff


Question:

Connor

Can someone please tell me the formula to work out the following question? I'm stumped. Thanks in advance.

Divide $312 so that:
(a) Doris gets twice what Dennis gets
(b) Dennis gets three times what Doris gets


Answer:

(a) Doris gets twice what Dennis gets

x = amount Dennis receives

y = amount Doris receives


There are two equations with two unknowns:

Doris (y) gets twice what Dennis (x) gets

1st equation: y = 2x

Doris (y) also gets $312 minus the amount Dennis (x) gets

2nd equation: y = 312 - x


Substitute 2x for the y in the 2nd equation

y = 312 - x

2x = 312 - x


You now have ONE EQUATION with ONE UNKNOWN


Solve for x


Add x to each side of the equation to remove the x from the right side of the equation

2x + x = 312 - x + x

3x = 312 + 0

3x = 312


Divide each side of the equation by 3 to remove the 3 from the left side of the equation

3x/3 = 312/3

x * (3/3) = 312/3

x * (1) = 312/3

x = 312/3

x = 104


Solve for y

Substitute 104 for x in the 1st equation

y = 2x

y = 2 * 104

y = 208


>>> the final answer to (a) is:

x = amount Dennis receives = $104

y = amount Doris receives = $208




(b) Dennis gets three times what Doris gets

x = amount Dennis receives

y = amount Doris receives


There are two equations with two unknowns:

Dennis (x) gets three times what Doris (y) gets

1st equation: x = 3y

Dennis (x) also gets $312 minus the amount Doris (y) gets

2nd equation: x = 312 - y


Substitute 3y for the x in the 2nd equation


x = 312 - y

3y = 312 - y

You now have ONE EQUATION with ONE UNKNOWN

Solve for y

Add y to each side of the equation to remove the y from the right side of the equation


3y + y = 312 - y + y

4y = 312 + 0

4y = 312

Divide each side of the equation by 4 to remove the 4 from the left side of the equation

4y/4 = 312/4

y * (4/4) = 312/4

y * (1) = 312/4

y = 312/4

y = 78


Solve for x


Substitute 78 for y in the 1st equation


x = 3y

x = 3 * 78

x = 234



>>> the final answer to (b) is:

x = amount Dennis receives = $234

y = amount Doris receives = $78




Thanks for writing.

Staff
www.solving-math-problems.com



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