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Just Equations
Break-Even Point
Bills and Coins
Mixtures
Investment
100
Equation 1: x+y=22 Equation 2: 4x-3y=-3
(9 , 13)
100
Shirt Manufacturer: Cost: y=10x+300 Income: y=40x
Break-Even Point: (10 , 400)
100
x=quarters, y=dimes Number Equation: x+y=18 Value Equation: 0.25x+0.10y=3 How many quarters and how many dimes?
8 quarters, 10 dimes
100
x=Sumatra coffee; y= Columbian coffee Pounds Equation: x+y=50 Price Equation: 2.50x+3.75y=167.50 How many pounds of Sumatra coffee? How many pounds of Columbian coffee?
16 pounds of Sumatra Coffee, 34 pounds of Columbian coffee
100
x=savings; y=money market Investment Equation: x+y=9885 Interest equation: 0.06x+0.095y=696.35 How much is invested in savings? How much is invested in the money market?
$6443 in savings, $3442 in money market
200
Equation 1: y-6x=-11 Equation 2: -2x-3y=-7
(2 , 1)
200
Phone Salesman Cost: $3000 general and $25/phone Income: $150/phone
Break-Even Point: 24 phones, income/cost of $3600
200
x=$5 bills, y=$10 bills Number Equation: x+y=210 Value Equation: 5x+10y=2000 How many $5 bills? How many $10 bills?
20 $5 bills, 190 $10 bills
200
x=hazelnuts; y=cashews Pounds Equation: x+y=60 Price Equation: 6.50x+4.50y=306 How many pounds of hazelnuts? How many pounds of cashews?
18 pounds of hazelnuts, 42 pounds of cashews
200
x=savings, y=checking Investment Equation: x+y=15,600 Interest equation: 0.08x+0.09y=1334.28 How much in savings? How much in checking?
$2324 in savings, $13276 in checking
300
Equation 1: y+7=5x Equation 2: -3x-2y=-12
(2 , 3)
300
Sandwich Concessions I spend $500 on general supplies and $0.50 per sandwich. I sell the sandwiches for $3.00/each. How many sandwiches do I need to make to break even?
200 sandwiches.
300
Number equation: I have a total of 1156 coins saved up in nickels (x) and pennies (y). Value Equation: The nickels (0.05x) and pennies (0.01y) add up to $41.72. How many nickels? How many pennies?
754 nickels, 402 pennies
300
Pounds equation: Janice is making a mixture of rose tea (x) and orange tea (y) that is going to weigh 3 pounds all together. Price equation: The rose tea is $10.20/pound (10.20x) while the orange tea is $13.60/pound (13.60y) and altogether, it is going to cost $34. How many pound of rose tea? How many pounds of orange tea?
2 pounds of rose tea, 1 pound of orange tea
300
x=secure bond, y= stock venture Investment Equation: x+y=20449 Interest Equation: 0.025x+0.034y=623.05 How much in the secure bond? how much in the stock venture?
$8024 in the secure bond, $12425 in the stock venture
400
Equation 1: x+y=586 Equation 2: 12.95x+17.95y=9423.70
(219 , 367)
400
Hats Jaurice makes hats. He bought a sewing machine for $300. He spends $20 making each hat. He can then sell the hats for $50/each. How many hats should he sell to break even?
10 hats.
400
Number Equation: The "Sharks" have a total of 201 bills in $20 bills (x) and $100 bills (y) from my concessions stand. Value Equation: The $20 bills (20x) and $100 bills (100y) are worth $10260 all together. How many $20 bills? How many $100 bills?
123 $20 bills, 78 $100 bills
400
Ounces Equation: I am making a hot cocao blend that contains cocao powder (x) and sugar (y) and weighs 12 ounces all together. Price equation: The cocao powder is $1.25/oz (1.25x) and the sugar is $0.25/oz (0.25x) and will cost $11 all together. How many ounces of cocao powder? How many ounces of sugar?
8 oz of cocao powder, 4 oz sugar.
400
x=bank of America, y=Freedom Credit Union Investment Equation: x+y=1500 Interest Equation: 0.05x+0.06y=500 How much in Bank of America? how much in Freedom Credit Union?
$1500 in Bank of America, $500 in Freedom Credit Union
500
Equation 1: 5x+10y=300 Equation 2: 30y-20x=200
(20 , 20)
500
Greeting Cards Dan started a greeting card business when he invested $450 into it. He spends $0.15 to make each card. He then sells each card for $4.65. How many cards does Dan make to break even and what is his income/cost at this point?
100 cards. Income/cost = $465
500
I found 385 coins in my couch. They are ALL nickels and dimes. They are worth $29.50. How many nickels did I find? How many dimes did I find?
180 nickels, 205 dimes
500
I need to buy and mix Koolaid and sugar to make punch for a block party. Alltogether, I need 35 lbs of the mix. The Koolaid costs $10/lb and the sugar costs $2/lb. I spend a total of $246. How many pounds of Koolaid did I buy? How many pounds of sugar did I buy?
22lbs of Koolaid, 13lbs of sugar
500
An investment banker puts $150000 in two stocks - Apple (x) and Gold (y). Apple's interest rate is 1.5% (0.015x) and Gold's interest rate is 4% (0.045y). He makes $2569 in one year. How much did he invest in Apple? How much did he invest in Gold?
$139367 in Apple, $10633 in Gold