Quant: Translations Flashcards
What is the most common mistake when translating to equations?
BACKWARDS
e.g. There are three times as many women as men.
3W = M –> NO!
There are MORE women –> W = 3M
Also, watch out for POSITIVES vs NEGATIVES, and PARENTHESES when substituting
Be MINDFUL of POTENTIAL ERRORS, and CHECK your work!
Joe is 6 years older than Mike. In 3 years, he will be twice as old as Mike. How old will Joe be in 3 years?
12
(1) J = M + 6
(2) J + 3 = 2 (M + 3) (REMEMBER PARENTHESES!)
Substitute J from (1) into (2):
M + 6 + 3 = 2M + 6
3 = M
It asks for JOE IN 3 YEARS –> J + 3
J = M + 6 = 9
J + 3 = 12
The average of 5, 9, and 2x is 12. What is x?
S = AN (Sum = Average * Number of Numbers)
Sum = 12 * 3 = 36
5 + 9 + 2x = 36
2x = 22
x = 11
5 sisters collect 35 shells. If the youngest collected 5 fewer than the other 4 sisters combined, how many did the youngest collect?
15
Let Y = youngest, and C = other 4 sisters combined
Y + C = 35
Y = C - 5
rearrange (2) –> C = Y + 5
substitute into (1) –> Y + (Y + 5) = 35
2Y = 30
Y = 15
Joe earns $10 for each ticket sold, plus a bonus of $3 for each ticket he sells over the first 200 tickets. If he was paid $4600, how many tickets did he sell?
T = 400
General formula: R = PQ (Revenue = Price * Quantity)
Revenue = (base pay per ticket * total # tickets) + (bonus per ticket * # bonus tickets)
4600 = 10T + 3(T - 200)
4600 = 13T - 600
5200 = 13T
T = 400
(These numbers are used in real life with cards – there are 52 cards, including 13 of each of the 4 suits)
A store sold 200 TVs at a total price of X dollars. If each TV was bought for 25% below the selling price per TV, then, in terms of X, for how many dollars was each TV bought?
Selling price per TV = Total Price / Quantity = X / 200
Bought for 25% less –> multiply by 3/4
X / 200 * 3/4 = 3X / 800
