C. ⅓of Jose’s money is equal to ¼ of Diwa’s money. 1) Find the ratio of Jose’s money to Diwa’s money. 2) What is the ratio of the total amount of money to Jose’s money? 3) What fraction of the total amount of money is Diwa’s money?
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Answer:
To solve the given problem, let's denote Jose's money as J and Diwa's money as D.
1) The given information states that 1/3 of Jose's money is equal to 1/4 of Diwa's money. Mathematically, this can be represented as:
1/3 * J = 1/4 * D
To find the ratio of Jose's money to Diwa's money, we can divide both sides of the equation by 1/4:
(1/3 * J) / (1/4) = (1/4 * D) / (1/4)
This simplifies to:
J / (1/3) = D / 1
J / (1/3) = D
Thus, the ratio of Jose's money to Diwa's money is J : D = 1 : 1/3, which can also be expressed as 3 : 1.
2) The total amount of money is the sum of Jose's money and Diwa's money. The ratio of the total amount of money to Jose's money can be found by dividing the total amount by Jose's money. Mathematically, this can be represented as:
(J + D) / J
Since J = D/3 (from the previous equation), we can substitute this into the expression:
(J + D) / J = (D/3 + D) / (D/3)
Simplifying further:
(D + 3D) / (D/3) = 4D / (D/3) = 12
Therefore, the ratio of the total amount of money to Jose's money is 12 : 1.
3) To find the fraction of the total amount of money that represents Diwa's money, we divide Diwa's money by the total amount of money:
D / (J + D)
Substituting J = D/3 into the expression:
D / (D/3 + D) = D / (4D/3) = 3/4
Thus, Diwa's money represents 3/4 of the total amount of money.
Step-by-step explanation:
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