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 an augmented matrix, and fill in the blanks.\newlineYesterday a chef used 3232 eggs to make 44 chocolate souffles and 66 lemon meringue pies. The day before, he made 11 chocolate souffle, which used 55 eggs. How many eggs does each dessert require?\newlineA chocolate souffle requires ____\_\_\_\_ eggs and a lemon meringue pie requires ____\_\_\_\_ eggs.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right 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 an augmented matrix, and fill in the blanks.\newlineYesterday a chef used 3232 eggs to make 44 chocolate souffles and 66 lemon meringue pies. The day before, he made 11 chocolate souffle, which used 55 eggs. How many eggs does each dessert require?\newlineA chocolate souffle requires ____\_\_\_\_ eggs and a lemon meringue pie requires ____\_\_\_\_ eggs.
  1. Define Variables: Let xx be the number of eggs needed for a chocolate souffle and yy be the number of eggs needed for a lemon meringue pie. We can write two equations based on the information given:
  2. Write Equations: Equation for yesterday: 4x+6y=324x + 6y = 32 (since 44 souffles and 66 pies were made using 3232 eggs).
  3. Convert to Matrix: Equation for the day before: 1x=51x = 5 (since 11 souffle was made using 55 eggs).
  4. Eliminate Variables: Now we have the system of equations:\newline11. 4x+6y=324x + 6y = 32\newline22. x=5x = 5
  5. Solve for yy: Convert the system of equations into an augmented matrix:\newline[4amp;6amp;∣amp;32 1amp;0amp;∣amp;5]\begin{bmatrix} 4 & 6 & | & 32 \ 1 & 0 & | & 5 \end{bmatrix}
  6. Substitute and Find xx: Use the second equation to eliminate xx from the first equation by multiplying the second equation by −4-4 and adding it to the first equation:\newline\(-4\times\begin{bmatrix}11 & 00 | & 55\end{bmatrix} = \begin{bmatrix}−4-4 & −0-0 | & −20-20\end{bmatrix}(\newline\)\begin{bmatrix}44 & 66 | & 3232\end{bmatrix} + \begin{bmatrix}−4-4 & −0-0 | & −20-20\end{bmatrix} = \begin{bmatrix}00 & 66 | & 1212\end{bmatrix}
  7. Final Results: Now we have the new system in matrix form: [4amp;6amp;∣amp;32 0amp;6amp;∣amp;12]\begin{bmatrix} 4 & 6 & \vert & 32 \ 0 & 6 & \vert & 12 \end{bmatrix}
  8. Final Results: Now we have the new system in matrix form:\newline[4amp;6 0amp;6][32 12]\begin{bmatrix}4 & 6 \ 0 & 6 \end{bmatrix}\begin{bmatrix}32 \ 12 \end{bmatrix}Divide the second row by 66 to solve for yy:\newline[0amp;6 12]÷6=[0amp;1 2]\begin{bmatrix}0 & 6 \ 12 \end{bmatrix} \div 6 = \begin{bmatrix}0 & 1 \ 2 \end{bmatrix}\newlineSo, y=2y = 2.
  9. Final Results: Now we have the new system in matrix form:\newline\begin{bmatrix}4 & 6 \ 0 & 6\end{bmatrix}\begin{bmatrix}32\12\end{bmatrix}Divide the second row by 66 to solve for yy:\newline[0amp;6 12]÷6=[0amp;1 2]\begin{bmatrix}0 & 6 \ 12\end{bmatrix} \div 6 = \begin{bmatrix}0 & 1 \ 2\end{bmatrix}\newlineSo, y=2y = 2.Substitute y=2y = 2 into the second original equation, x=5x = 5, to find xx. But since xx is already given as 55, there's no need to substitute, and we can say x=5x = 5.
  10. Final Results: Now we have the new system in matrix form:\newline4amp;6amp;∣amp;32 0amp;6amp;∣amp;12\begin{matrix} 4 & 6 & | & 32 \ 0 & 6 & | & 12 \end{matrix}Divide the second row by 66 to solve for yy:\newline0amp;6amp;∣amp;12\begin{matrix} 0 & 6 & | & 12 \end{matrix} ÷6=0amp;1amp;∣amp;2\div 6 = \begin{matrix} 0 & 1 & | & 2 \end{matrix}\newlineSo, y=2y = 2.Substitute y=2y = 2 into the second original equation, x=5x = 5, to find xx. But since xx is already given as 55, there's no need to substitute, and we can say x=5x = 5.Therefore, a chocolate souffle requires 55 eggs and a lemon meringue pie requires yy11 eggs.

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 5 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 5 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 5 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 5 months ago

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

Posted 8 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 8 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 5 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 5 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 5 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 5 months ago

View all (31)

Related topics

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