The Grass Doctor

How to Solve these weighted averages problems (step by step please)?

I don't know how to solve these problems can someone write the step-by-step explanation with the answers. 1. Maple Middle School sold gift wrap for a fund raiser. The gift wrap in solid colors sold for $4.00 a roll, and the total amount of money collected was $2,340. How many rolls of each kind of gift wrap were sold? 2. Brandy owns a specialty coffee store. She wants to create a special mix using two coffees, one priced at $6.40 per pound and the other priced at 7.28 per pound. How many pounds of the $7.28 coffee should she mix with 9 pounds of the $6.40 coffee to sell the mixture for $6.95 per pound? 3. Darius sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound. To make his mixture, he uses Virginia peanuts that costs $3.50 per pound and Spanish peanuts that cost $3.00 per pound. He mixes 10 pounds at a time. 4. A nursery sells Kentucky Blue Grass seeds fir $5.75 per pound and Tall Fescue seeds for $4.50 per pound. The nursery sells a mixture of the two kinds of seeds for $5.25 per pound. Let k represent the amount of Kentucky Blue Grass seed the nursery uses in 5 pounds of mixture.

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1. 1. Maple Middle School sold gift wrap for a fund raiser. The gift wrap in solid colors sold for $4.00 a roll, and the total amount of money collected was $2,340. How many rolls of each kind of gift wrap were sold? You left out the cost for the other gift wrap, so I can't help you with this one until I get more info. ~~~~~~~~~~~~~~~~~~ 2. Brandy owns a specialty coffee store. She wants to create a special mix using two coffees, one priced at $6.40 per pound and the other priced at $7.28 per pound. How many pounds of the $7.28 coffee should she mix with 9 pounds of the $6.40 coffee to sell the mixture for $6.95 per pound? HINT: Write what you know in a table. Type …………. Qty …………. Cost …………. Total $7.28/lb. coffee …………. x …………. 7.28 …………. x * 7.28 = 7.28x $6.40/lb. coffee …………. 9 …………. 6.4 …………. 9 * 6.4 = 57.6 Total …………. x + 9 …………. 6.95 …………. (x + 9) * 6.95 = 6.95(x + 9) The first 2 rows of the last column always add up to the third row in that column. 7.28x + 57.6 = 6.95(x + 9) Distribute and solve. 7.28x + 57.6 = 6.95(x) + 6.95(9) 7.28x + 57.6 = 6.95x + 62.55 57.6 - 62.55 = 6.95x - 7.28x -4.95 = -0.33x 15 = x ANSWER: You need 15 kg of the $7.28/lb. coffee. ~~~~~~~~~~~~~~~~~~ 3. Darius sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound. To make his mixture, he uses Virginia peanuts that costs $3.50 per pound and Spanish peanuts that cost $3.00 per pound. He mixes 10 pounds at a time. HINT: Write what you know in a table. Type …………. Qty …………. Cost …………. Total Virginia peanuts …………. a …………. 3.5 …………. a * 3.5 = 3.5a Spanish peanuts …………. b …………. 3 …………. b * 3 = 3b Total …………. a + b …………. 3.4 …………. (a + b) * 3.4 = 3.4(a + b) The first 2 rows of the last column always add up to the third row in that column. 3.5a + 3b = 3.4(a + b) Given: Mixture is 10 lbs. Means: a + b = 10 Replace (x + y) with 10 and simplify. 3.5a + 3b = 3.4(a + b) 3.5a + 3b = 3.4(10) 3.5a + 3b = 34 You now have 2 equations. 3.5a + 3b = 34 a + b = 10 Solve the 2nd one for y. a + b = 10 b = 10 - a Replace y with 10 - a in the 1st one. 3.5a + 3b = 34 3.5a + 3(10 - a) = 34 3.5a + 30 - 3a = 34 3.5a - 3a = 34 - 30 0.5a = 4 a = 4 / 0.5 a = 8 Substitute a with 8 in b = 10 - a to find b. b = 10 - a b = 10 - 8 b = 2 You need 8 lbs. of the Virginia peanuts and 2 lbs. of the Spanish peanuts to make a 10-lb. mixture worth $3.40 per lbs.. ~~~~~~~~~~~~~~~~~~ 4. A nursery sells Kentucky Blue Grass seeds for $5.75 per pound and Tall Fescue seeds for $4.50 per pound. The nursery sells a mixture of the two kinds of seeds for $5.25 per pound. Let k represent the amount of Kentucky Blue Grass seed the nursery uses in 5 pounds of mixture. HINT: Write what you know in a table. Type …………. Qty …………. Cost …………. Total Kentucky Blue Grass seeds …………. a …………. 5.75 …………. a * 5.75 = 5.75a Tall Fescue seeds …………. b …………. 4.5 …………. b * 4.5 = 4.5b Total …………. a + b …………. 5.25 …………. (a + b) * 5.25 = 5.25(a + b) The first 2 rows of the last column always add up to the third row in that column. 5.75a + 4.5b = 5.25(a + b) Given: Mixture is 5 lbs. Means: a + b = 5 Replace (x + y) with 5 and simplify. 5.75a + 4.5b = 5.25(a + b) 5.75a + 4.5b = 5.25(5) 5.75a + 4.5b = 26.25 You now have 2 equations. 5.75a + 4.5b = 26.25 a + b = 5 Solve the 2nd one for y. a + b = 5 b = 5 - a Replace y with 5 - a in the 1st one. 5.75a + 4.5b = 26.25 5.75a + 4.5(5 - a) = 26.25 5.75a + 22.5 - 4.5a = 26.25 5.75a - 4.5a = 26.25 - 22.5 1.25a = 3.75 a = 3.75 / 1.25 a = 3 Substitute a with 3 in b = 5 - a to find b. b = 5 - a b = 5 - 3 b = 2 You need 3 lbs. of the Kentucky Blue Grass seeds and 2 lbs. of the Tall Fescue seeds to make a 5-lb. mixture worth $5.25 per lb.