Word Problems?

Question

Problem 1:Cindy has 30 coins, consisting of dimes and quarters, that total $5.10. How many coins of each kind does she have?


Problem 2:For moving purposes the Hendersons bought 27 cardboard boxes for $78.50. There were two kinds of boxes; the large ones cost $5.50 per box and the small ones were $ 2.00 per box. How many boxes of each kind did they buy?

Problem 3:Suppose that one solution contains 50 % alcohol and another solution contains 80% alcohol. How many liters of each solution should be mixed to make 4.5 liters of a 70 %alcohol solution?

I could come up with a answer to 1 of these i was wondering if anyone knew how to solve all or 1 or 2. thanks for your time

Answer 1

Problem 1:

Solve two simultaneous equations.

10d + 25q = 510
d + q = 30

d = 30 - q

10(30 - q) + 25q = 300 - 10q + 25q = 300 + 15q = 510
15q = 210
q = 14
d = 30 - q = 30 - 14 = 16

There are 16 dimes and 14 quarters.

You can solve the rest yourself.

Answer 2

# 2, Divide total cost by larger box price ; 78.5/5.5= 39.5. Then divide that by 5.5. That gives you how many large boxes (drop the remainder) Minus # of lb's from box total = # of small boxes

Answer 3

1)
x + y = 30
.1x + .25y = 5.1

.1x + .25(30-x) = 5.1

.1x + 7.5 - .25x = 5.1

-.15x = -2.4

x = 16 dimes
y = 14 quarters
------------------------
2)
x+y=27
5.5x + 2y = 78.5

5.5(27-y) + 2y = 78.5

148.5 - 5.5y + 2y = 78.5

-3.5y = -70

y = 20 - $2.00 boxes
x = 7 - $5.50 boxes

--------------------------
3)
x+y=4.5
.5x+.8y=.7(4.5)

.5(4.5-y) + .8y = 3.15

2.25 - .5y + .8y = 3.15

.3y = .9

y = 3 liters 80%
x = 1.5 liters 50%

Answer 4

4x.25=1.00
5x4=20 quarters
1 dime.