Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineA coffee shop is having a sale on prepackaged coffee and tea. Yesterday they sold 2525 packages of coffee and 3939 packages of tea, for which customers paid a total of $587\$587. The day before, 1010 packages of coffee and 3939 packages of tea was sold, which brought in a total of $422\$422. How much does each package cost?\newlinePer package, coffee costs $____\$\_\_\_\_ and tea costs $____\$\_\_\_\_.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Solve a system of equations using elimination: word problemsright chevron icon

Full solution

Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineA coffee shop is having a sale on prepackaged coffee and tea. Yesterday they sold 2525 packages of coffee and 3939 packages of tea, for which customers paid a total of $587\$587. The day before, 1010 packages of coffee and 3939 packages of tea was sold, which brought in a total of $422\$422. How much does each package cost?\newlinePer package, coffee costs $____\$\_\_\_\_ and tea costs $____\$\_\_\_\_.
  1. Equation 11: Let's denote the price of each package of coffee as cc and the price of each package of tea as tt. From the first day's sales, we have the equation 25c+39t=58725c + 39t = 587. This represents the total amount earned from selling 2525 packages of coffee and 3939 packages of tea.
  2. Equation 22: From the sales of the day before, we have the equation 10c+39t=42210c + 39t = 422. This represents the total amount earned from selling 1010 packages of coffee and 3939 packages of tea.
  3. Elimination Method: We now have a system of two equations:\newline11. 25c+39t=58725c + 39t = 587\newline22. 10c+39t=42210c + 39t = 422\newlineWe will use elimination to solve this system. To eliminate tt, we can subtract the second equation from the first equation.
  4. Subtraction Result: Subtracting the second equation from the first, we get:\newline(25c+39t)−(10c+39t)=587−422(25c + 39t) - (10c + 39t) = 587 - 422\newlineThis simplifies to:\newline15c=16515c = 165
  5. Coffee Price Calculation: Dividing both sides of the equation 15c=16515c = 165 by 1515, we find the price of each package of coffee:\newlinec=16515c = \frac{165}{15}\newlinec=11c = 11
  6. Tea Price Calculation: Now that we know c=11c = 11, we can substitute this value into one of the original equations to find tt. We'll use the second equation:\newline10c+39t=42210c + 39t = 422\newlineSubstituting cc with 1111 gives us:\newline10(11)+39t=42210(11) + 39t = 422
  7. Tea Price Calculation: Now that we know c=11c = 11, we can substitute this value into one of the original equations to find tt. We'll use the second equation:\newline10c+39t=42210c + 39t = 422\newlineSubstituting cc with 1111 gives us:\newline10(11)+39t=42210(11) + 39t = 422 Solving for tt, we get:\newline110+39t=422110 + 39t = 422\newlineSubtracting 110110 from both sides gives us:\newline39t=422−11039t = 422 - 110\newlinett00
  8. Tea Price Calculation: Now that we know c=11c = 11, we can substitute this value into one of the original equations to find tt. We'll use the second equation:\newline10c+39t=42210c + 39t = 422\newlineSubstituting cc with 1111 gives us:\newline10(11)+39t=42210(11) + 39t = 422 Solving for tt, we get:\newline110+39t=422110 + 39t = 422\newlineSubtracting 110110 from both sides gives us:\newline39t=422−11039t = 422 - 110\newlinett00 Dividing both sides of the equation tt00 by tt22, we find the price of each package of tea:\newlinett33\newlinett44

More problems from Solve a system of equations using elimination: word problems

Question
Solve using substitution. 5x−2y=−7 5x - 2y = -7 x=−5 x = -5 (_,_)
Get tutor helpright-arrow

Posted 6 months ago

Question
Is (1,1)(1,1) a solution to this system of equations? \newline4x+10y=144x + 10y = 14\newlinex+6y=7x + 6y = 7\newlineChoices:\newline(A) yes \newline(B) no
Get tutor helpright-arrow

Posted 6 months ago

Question
Which describes the system of equations below?\newliney=–3x+9y = –3x + 9 \newliney=–3x+9y = –3x + 9 \newlineChoices:\newline(A) consistent and independent\text{(A) consistent and independent} \newline(B) consistent and dependent\text{(B) consistent and dependent} \newline(C) inconsistent\text{(C) inconsistent}
Get tutor helpright-arrow

Posted 6 months ago

Question
Solve using elimination. \newline7x−8y=−17 7x - 8y = -17 \newline −7x+3y=2 -7x + 3y = 2 \newline (____,____)(\_\_\_\_, \_\_\_\_)
Get tutor helpright-arrow

Posted 6 months ago

Question
Solve. \newlinex=−2 x = -2 \newline−2x+2y=−8 -2x + 2y = -8 \newline(____,____)(\_\_\_\_, \_\_\_\_)
Get tutor helpright-arrow

Posted 10 months ago

Question
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineAt a community barbecue, Mrs. Wilkerson and Mr. Hogan are buying dinner for their families. Mrs. Wilkerson purchases 33 hot dog meals and 33 hamburger meals, paying a total of $36\$36. Mr. Hogan buys 11 hot dog meal and 33 hamburger meals, spending $26\$26 in all. How much do the meals cost?\newlineHot dog meals cost $\$_______ each, and hamburger meals cost $\$________ each.
Get tutor helpright-arrow

Posted 10 months ago

Question
Solve the system of equations by substitution.\newline−3x−y−3z=−11-3x - y - 3z = -11\newlinez=5z = 5\newlinex−y+3z=19x - y + 3z = 19\newline(____.____,____)
Get tutor helpright-arrow

Posted 6 months ago

Question
Solve the system of equations by elimination.\newlinex−3y−2z=10 x - 3y - 2z = 10 \newline3x+2y+2z=14 3x + 2y + 2z = 14 \newline2x−3y−2z=16 2x - 3y - 2z = 16 \newline(_,_,_)(\_,\_,\_)
Get tutor helpright-arrow

Posted 6 months ago

Question
Solve the system of equations.\newliney=x2+36x+3 y = x^2 + 36x + 3 \newliney=22x−37 y = 22x - 37 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_)(\_,\_)\newline(_,_)(\_,\_)
Get tutor helpright-arrow

Posted 6 months ago

Question
Solve the system of equations.\newliney=−x−24 y = -x - 24 \newlinex2+y2=488 x^2 + y^2 = 488 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_) (\_,\_) \newline(_,_) (\_,\_)
Get tutor helpright-arrow

Posted 6 months ago

View all (43)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant