Solving systems that compare numbers. Game on.

Solving systems that compare numbers is a grade 9 math skill aligned to Common Core standard HSA.REI.C.6: solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 solving systems that compare numbers problems our math games drill.

CCSS HSA.REI.C.610 questions in the bank
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Warm-upmedium

A rope with a length of 2828 meters is cut into two parts. One part has a length of aa meters, and the other part has a length of bb meters. The value of aa is 44 more than 33 times the value of bb. What is the value of aa?

The parts add to 2828, so a+b=28a + b = 28. Also a=3b+4a = 3b + 4. Substitute: (3b+4)+b=28(3b + 4) + b = 28, so 4b+4=284b + 4 = 28, 4b=244b = 24, and b=6b = 6. Then a=3(6)+4=22.a = 3(6) + 4 = 22\textsf{.}

Mid-gamemedium

A stick with a length of 4545 inches is cut into two parts. One part has a length of mm inches, and the other part has a length of nn inches. The value of mm is 55 more than 44 times the value of nn. What is the value of mm?

The parts add to 4545, so m+n=45m + n = 45. Also m=4n+5m = 4n + 5. Substitute: (4n+5)+n=45(4n + 5) + n = 45, so 5n+5=455n + 5 = 45, 5n=405n = 40, and n=8n = 8. Then m=4(8)+5=37.m = 4(8) + 5 = 37\textsf{.}

Mid-gamemedium

A cable with a length of 4848 yards is cut into two parts. One part has a length of rr yards, and the other part has a length of ss yards. The value of rr is 66 more than 22 times the value of ss. What is the value of rr?

The parts add to 4848, so r+s=48r + s = 48. Also r=2s+6r = 2s + 6. Substitute: (2s+6)+s=48(2s + 6) + s = 48, so 3s+6=483s + 6 = 48, 3s=423s = 42, and s=14s = 14. Then r=2(14)+6=34.r = 2(14) + 6 = 34\textsf{.}

Mid-gamemedium

A pipe with a length of 6060 centimeters is cut into two parts. One part has a length of uu centimeters, and the other part has a length of vv centimeters. The value of uu is 44 more than 33 times the value of vv. What is the value of uu?

The parts add to 6060, so u+v=60u + v = 60. Also u=3v+4u = 3v + 4. Substitute: (3v+4)+v=60(3v + 4) + v = 60, so 4v+4=604v + 4 = 60, 4v=564v = 56, and v=14v = 14. Then u=3(14)+4=46.u = 3(14) + 4 = 46\textsf{.}

Mid-gamemedium

A fence rail with a length of 5050 feet is cut into two parts. One part has a length of cc feet, and the other part has a length of dd feet. The value of cc is 22 more than 33 times the value of dd. What is the value of cc?

The parts add to 5050, so c+d=50c + d = 50. Also c=3d+2c = 3d + 2. Substitute: (3d+2)+d=50(3d + 2) + d = 50, so 4d+2=504d + 2 = 50, 4d=484d = 48, and d=12d = 12. Then c=3(12)+2=38.c = 3(12) + 2 = 38\textsf{.}

Mid-gamemedium

A length of yarn measuring 3535 meters is cut into two parts. One part has a length of ee meters, and the other part has a length of ff meters. The value of ee is 55 more than 22 times the value of ff. What is the value of ee?

The parts add to 3535, so e+f=35e + f = 35. Also e=2f+5e = 2f + 5. Substitute: (2f+5)+f=35(2f + 5) + f = 35, so 3f+5=353f + 5 = 35, 3f=303f = 30, and f=10f = 10. Then e=2(10)+5=25.e = 2(10) + 5 = 25\textsf{.}

Mid-gamemedium

A string with a length of 6464 inches is cut into two parts. One part has a length of gg inches, and the other part has a length of hh inches. The value of gg is 44 more than 55 times the value of hh. What is the value of hh?

The parts add to 6464, so g+h=64g + h = 64. Also g=5h+4g = 5h + 4. Substitute: (5h+4)+h=64(5h + 4) + h = 64, so 6h+4=646h + 4 = 64, 6h=606h = 60, and h=10.h = 10\textsf{.}

Buzzer beatermedium

A roll of tape with a length of 5555 centimeters is cut into two parts. One part has a length of jj centimeters, and the other part has a length of kk centimeters. The value of jj is 55 more than 44 times the value of kk. What is the value of jj?

The parts add to 5555, so j+k=55j + k = 55. Also j=4k+5j = 4k + 5. Substitute: (4k+5)+k=55(4k + 5) + k = 55, so 5k+5=555k + 5 = 55, 5k=505k = 50, and k=10k = 10. Then j=4(10)+5=45.j = 4(10) + 5 = 45\textsf{.}

Tests that cover solving systems that compare numbers:
PSAT 8/9SATNAEPNY State MathMCAP
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