sat suite question viewer

Algebra / Systems of two linear equations in two variables Difficulty: Hard

A piece of wire with a length of $32$ inches is cut into two parts. One part has a length of $x$ inches, and the other part has a length of $y$ inches. The value of $x$ is $4$ more than $3$ times the value of $y$ . What is the value of $x$ ?

Back question 86 of 112 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112

Explanation

The correct answer is $25$ . It’s given that a piece of wire has a length of $32$ inches and is cut into two parts. It’s also given that one part has a length of $x$ inches and the other part has a length of $y$ inches. It follows that the equation $x + y = 32$ represents this situation. It’s also given that the value of $x$ is $4$ more than $3$ times the value of $y$ , or $x = 3 y + 4$ . Substituting $3 y plus 4$ for $x$ in the equation $x + y = 32$ yields $3 y + 4 + y = 32$ . Combining like terms on the left-hand side of this equation yields $4 y + 4 = 32$ . Subtracting $4$ from both sides of this equation yields $4 y equals 28$ . Dividing both sides of this equation by $4$ yields $y equals 7$ . Substituting $7$ for $y$ in the equation $x = 3 y + 4$ yields $x = 3 (7) + 4$ , or $x equals 25$ . Therefore, the value of $x$ is $25$ .