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Intermediate Algebra Name yN^U Chapter 4.3: Solving Applications of Systems of Linear Equations in 3 Variables 0
- Say you went out trick-or-treatmg and received 24 pieces candy. The number of Tootsie-Pops you got is two less than twice the number of pieces of Snickers. The number of Starbursts is two more than five times the number of pieces of Snickers. How many pieces of Snickers, Tootsie-Pops, and Starbursts did you get?
Let u - \i)sMx(h Tcc-ili A^y^ '
Equation 1: Xtdrt^^^H
Equation 2: U x '2JC'X
Equation 3: t^^^^.
Answers: 3 = number of Snickers 4 = number of Tootsie-Pops 17 = number of Starbursts
- A 141-person crew is made up of inspectors, contractors, and laborers. The number of contractors is four more than the number of inspectors. The number of laborers is three less than eight times the number of inspectors. Determine the number of inspectors, contractors, and laborers on the crew.
Let \iicx\V>tA i;r\fi>^cx(A
Let - Vy\jiWKif\V \rx-
L e t j L _ - i\
Equation 1: K i U ^ ^ ^ Equation 2: u „ >CV^ Equation 3: _ * > ^
Answers: 14 = number of inspectors 18 = number of contractors 109 = number of laborers
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- At local stationary store 3 notebooks, 2 pencils, and 4 pens are sold for $6.13; 2 notebooks, 5 pencils, and 3 pens are sold for $5.50; and 1 notebook, 3 pencils, and 2 pens are sold for $3.12. What is the price of 1 notebook, 1 pencil, and 1 pen sold individually?^ [
Let • = I (H r\ (Aitl
L e t ^ = CV^ f\ s^ir\
Let ' • • ' ' ^ Equation 1:
Equation 2: 2 X - ^ 5 ^ i \ % ^ ^'^f-^'^
Answers: $1.29 = the cost of 1 notebook _ ^ 9'3.-V-^i7 C^^'CJf^» $0.35 = the cost of 1 pencil " ^-"^ ^ x. $0.39 = the cost of 1 pen
- A vendor at a rock concert needed tolceep t r a c ^ f the number of long-sleeve shirts, short-sleeve shirts, and tank-tops he sold at the concert, which sell for $16.99, $14.99, and $12.99, respectively. He completely forgot to keep track, but he knew he could figure it out. The register tape revealed that a total of 167 shirts were sold, which brought in a total of $2477.33. He also could tell from the empty boxes that he sold 7 more short-sleeve shirts than he did long-sleeve. How many shirts of each type did the vendor sell?
L e t = iWisvbv c\
Let U = &\r
Let ^ - ^ViMlf C AcT^rY^^.
Equation 1:
Equation 2: \bA ^)Cr Hft ^U^"^ ^tH'^'^ .?>
Equation 3: 1 ^ " "
Answers: 49 = the number of long-sleeve shirts sold ^ ^ - ^ Hf^^^C*^'
56 = the number of short-sleeve shirts sold 62 = the number of tank-tops sold
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7, Say you invested $70,000 into three accounts: part at a 2% simple interest rate, part at a 10% simple interest rate, and the remainder at a 6% simple mterest rate. The amount of money invested at 10% was twice as much as the amount invested at 2%, How much do you have invested in each account if the total interest gained on all three accounts in one year wa§,$4800?
Let X = A ^ t K H VxW £:^^d a \ ^ ^ ^
Let a
Let / - -mjs^ &l
Equation 1: )C V U ^ ^ - ^^QXC^
Equation 2: i i „ 2%- —~ "
Equations: ^ ^ ^ ^ ^. ^ ^ ^ ^ ^ ^ g ^
o4^=(^cc • -
Answers: $15,000 = the amount of money invested at 2% $30,000 = the amount of money invested at 10% $25,000 = the amount of money invested at 6%
- A 12% solution, a 14% solution, and a 30% solution of sulfuric acid are to be mixed to get 12 liters of a 20% solution. How many liters of each must be mixed if the volume of the H%o solution must be 2 liters less than the volume «f the 3 *** 3 %** solution?
L e t = O J h / i L e t ^ = i ^ ^ V K u O V ^fA^
Equationl: ) ^ V \ \ V ^ ^ ^ 2 - ^ y ^ - U - ^ - ^ ^ ^
Equation 3:
Equation 2:
3 liters = the amount of 14% solution r -^~rS~ v, /
5 liters = the amount of 30% solution \
. 2 ^ -.©"j =^ *
Answers; 4 liters = the amount of 12% solution
