Age Problems. Solutions.
One man is three times as old as another. Fifteen years ago the first was six times as old as the second. Find their ages now.
3x − 15 = 6(x − 15)
The older man is 75 years old, and the other man is 25 years old.
(−y+x)(x+y)
x2 − y2
A collection of 109 coins is made up of quarters, dimes, and nickels. There are 7 fewer dimes than quarters and 3 less than five times as many nickels as dimes. Find the amount of the collection.
If the number of quarters is x, the equation is x + (x − 7) + (5(x − 7) − 3) = 109. The amount of collection is $10.60.
The digits of a certain three-digit number are consecutive odd numbers. If the sum of the digits is 15, find the number.
If the first consecutive number is x, then the equation is x + x + 2 + x + 4 = 15.
The number is 357 or 375 or 537 or 573 or 735 or 753.
Write as an exponent with a base of a.
ana3
an + 3
Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now?
If Jane's current age is x,
the equation will be x + 8 − 20 = 3(x − 20).
Helen is 32 years old. Jane is 24 years old.
(−a+b)(b–a)
b2 − 2ab + a2
A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has 4 more of the twenties. The total value of the money is $305.00. Find the number of twenty-dollar bills.
If x is a number of $5, the equation will be 5x + 20(x + 4) = 305.
13 twenty − dollar bills.
A certain number exceeds 18 by as much as 44 exceeds the number. What is the number?
If the number is x, then the equation is x − 18 = 44 − x. The number is 31.
Write as an exponent with a base of a.
aam
am + 1
A child is 12 years old, and his father is 32 years older. In how many years will the age of the father be 2 times the age of the child?
If the number of years x,
then the equation is 2(12 + x) = 44 + x.
In 20 years.
(−b–c)(b–c)
c2 − b2
A man has $0.70 in dimes and nickels. He has 8 coins altogether. How many nickels does he have?
If x is a number of nickels, then the equation is 5x + 10(8 − x) = 70.
2 nickels.
0.5(2y–1)–(0.5–0.2y)+1=0
y = 0
Write as an exponent with a base of a.
a2am
am + 2
A pharmacist has a 12% solution of boric acid and a 20% solution of boric acid. How much of each must he use to make 80 grams of a 15% boric acid solution?
50 grams of 12% solution of boric acid and 30 grams of 20% solution of boric acid.
(x+y)(−x–y)
− x2 − 2xy − y2
A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has a total of 32 bills. The total value of the money is $430.00. Find the number of five-dollar bills that he has.
If the number of $5 is x, the equation is 5x + 20(32 − x) = 430.
Bank teller has 14 five − dollar bills.
3x–5(2–x)=54
x = 8
Write as an exponent with a base of a.
(a2)m
a2m
What weight of dry substance is in 150g of a 3% substance solution? What weight of an 8% solution can we have with the same weight of dry substance?
4.5g of dry substance and 56.25g of an 8% solution.
(x–y)(y–x)
− x2 + 2xy − y2
To finance a bridge costing $94,500, the state contributed twice as much as the county and the county contributed twice as much as the city. How much did each contribute?
If the city contributed is x, the equations will be 4x + 2x + x = 94500.
The state contributed $54,000, the county contributed $27,000, the city contributed $13,500
6+(2–4x)+5=3(1–3x)
x = −2
Write as an exponent with a base of a.
25a4·(3a3)2
225a10