Question 469436: 1. Jennifer is 3x as old as Tony. 2 years ago she was 4x as old as tony was then. How old is tony now.
2. Lisa is now 9 days older than tom. In 2 years lisa will be 2x as old as tom will be then. How many years old is lisa now.
3. A group of friends chipped in equally to buy a birthday present. Each person paid $8. If 2 more friends chipped in everyone would have paid only $7. How much did the gift cost?
Answer by ccs2011(207)   (Show Source):
You can put this solution on YOUR website! ************************************
1. Let J and T represent the respective ages of Jennifer and Tony
Write the given information as equations
J = 3T
(J-2) = 4(T-2)
Substitute 3T for J in 2nd equation
3T - 2 = 4(T-2)
Distribute
3T - 2 = 4T - 8
Subtract 4T on both sides
-T -2 = -8
Add 2 on both sides
-T = -6
Flip Signs
T = 6
Therefore Tony is 6 years old, Jennifer is 18 years old
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2. Let L and T represent the respective ages of Lisa and Tom
Write the given information as equations
(i think you had a typo, it should be 9 years not days)
L = T + 9
(L+2) = 2(T+2)
Substitute (T+9) for L in 2nd equation
(T+9)+2 = 2(T+2)
Distribute
T + 11 = 2T + 4
Subtract 2T on both sides
-T + 11 = 4
Subtract 11 on both sides
-T = -7
Flip Signs
T = 7
Therefore Tom is 7 years old, Lisa is 16 years old
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3. Each person paid equally
Let n be number of friends, g be cost of gift
g = 8n
g = 7(n+2)
Substitute 8n for g in 2nd equation
8n = 7(n+2)
Distribute
8n = 7n + 14
Subtract 7n on both sides
n = 14
Substitute value into 1st equation
g = 8*14 = 112
Therefore cost of the gift was $112
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