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 substitution, and fill in the blanks.\newlineGabriel and Wyatt each want to run for president of their school's student body council. In order to do so, they must collect a certain number of signatures and get a nomination. So far, Gabriel has 1515 signatures, and Wyatt has 1313. Gabriel is collecting signatures at an average rate of 88 per day, whereas Wyatt is averaging 99 signatures every day. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How long will that take? How many signatures will they both have?\newlineIn _\_ days, Gabriel and Wyatt will each have collected _\_ signatures.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Solve a system of equations using substitution: word problemsright chevron icon

Full solution

Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineGabriel and Wyatt each want to run for president of their school's student body council. In order to do so, they must collect a certain number of signatures and get a nomination. So far, Gabriel has 1515 signatures, and Wyatt has 1313. Gabriel is collecting signatures at an average rate of 88 per day, whereas Wyatt is averaging 99 signatures every day. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How long will that take? How many signatures will they both have?\newlineIn _\_ days, Gabriel and Wyatt will each have collected _\_ signatures.
  1. Define variables: Let's define the variables:\newlineLet xx be the number of days after which they will have the same number of signatures.\newlineLet yy be the total number of signatures each will have at that point.\newlineGabriel's equation can be written as:\newliney=8x+15y = 8x + 15\newlineWyatt's equation can be written as:\newliney=9x+13y = 9x + 13\newlineWe want to find the values of xx and yy that satisfy both equations simultaneously.
  2. Gabriel's equation: To solve the system using substitution, we can solve one of the equations for yy and then substitute that expression into the other equation. Let's solve Gabriel's equation for yy:y=8x+15y = 8x + 15
  3. Substitute Gabriel's equation: Now we substitute the expression for yy from Gabriel's equation into Wyatt's equation:\newline9x+13=8x+159x + 13 = 8x + 15
  4. Solve for x: Next, we solve for x:\newline9x+13=8x+159x + 13 = 8x + 15\newline9x−8x=15−139x - 8x = 15 - 13\newlinex=2x = 2
  5. Substitute xx into Gabriel's equation: Now that we have the value of xx, we can substitute it back into either Gabriel's or Wyatt's equation to find yy. Let's use Gabriel's equation:\newliney=8x+15y = 8x + 15\newliney=8(2)+15y = 8(2) + 15\newliney=16+15y = 16 + 15\newliney=31y = 31
  6. Final solution: We have found that in 22 days, Gabriel and Wyatt will each have collected 3131 signatures.

More problems from Solve a system of equations using substitution: 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 9 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 9 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 (41)

Related topics

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