Question 469436
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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