|
Question 99306: Can you please take a look at these 3 problems? They're brain rattling!
1. A carpentry shop makes dinner tables and coffee tables. Each week the shop must complete at least 9 dinner tables and 13 coffee tables to be shippeed to furniture stores. The shop can produce at most 30 dinner tables and coffee tables combined each week. If the shop sells dinner tables for $120 and coffee tables for $150, how many of each item should be produced for a maximum weekly income? What is the maximum weekly income?
2. Miguel's coin collection consists of dimes and quarters. If he has 53 coins worth $7.85, how many of each type of coin does he have?
3. Grain worth 65 cents per pound was mixed with grain worth 90 cents per pound to produce 20 pounds of a mixture worth 80 cents per pound. Find how many pounds of each was used.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. A carpentry shop makes dinner tables and coffee tables.
Each week the shop must complete at least 9 dinner tables and 13 coffee tables to be shipped to furniture stores.
The shop can produce at most 30 dinner tables and coffee tables combined each week.
If the shop sells dinner tables for $120 and coffee tables for $150, how many of each item should be produced for a maximum weekly income? What is the maximum weekly income?
--------
Let "d" be number of dinner tables; let "c" be number of coffee tables.
----------
d >= 9
c >= 13
c + d <= 30
------------------
Draw a c,d coordinate system; let the horizontal axis be c and the vertical d.
------------
Draw a vertical line at c=13
Draw a horizontal line at d=9
Draw the line d = -c + 30
Find the vertices of the enclosed area.
Using each c,d coordinate pair to determine which pair of numbers of
dining tables and coffee tables give a maximum value.
====================================
2. Miguel's coin collection consists of dimes and quarters. If he has 53 coins worth $7.85, how many of each type of coin does he have?
Let # of dimes = d and # of quarters be "q".
EQUATIONS:
Number Equation: d + q = 53
Value Equation: 10d + 25q = 785 cents
================
Use the two equations to solve for d and q.
=====================
3. Grain worth 65 cents per pound was mixed with grain worth 90 cents per pound to produce 20 pounds of a mixture worth 80 cents per pound. Find how many pounds of each was used.
Let amt. of 65 cent grain be "x" lbs ; Value is 65x cents.
Amt. of 90 cent grain is "20-x" lbs ; value is 90(20-x) = 1800-90x cents
---------
Amt of mixture is 20 lbs. ; Value is 80*20 = 1600 cents
--------------
EQUATION:
value + value = value
65x + 1800-90x = 1600
-25x = -200
x = 8 lbs (amount of 65 cent grain in the mixture)
20-8 = 12 lbs (amount of 90 cent grain in the mixture
=======================
Cheers,
Stan H.
|
|
|
| |
