Systems word problems with one value given Practice

Warm-upmedium

A cart holds $3$ -pound packages and $8$ -pound packages with a total weight of $67$ pounds. If there are $5$ of the $8$ -pound packages on the cart, how many $3$ -pound packages are on the cart?

The situation can be written as the system $\begin{cases} 3x + 8y = 67 \ y = 5 \end{cases}$ . Substitute $y = 5$ into the first equation: $3x + 8(5) = 67$ , so $3x + 40 = 67$ . Then $3x = 27$ and $x = 9$ .

Mid-gamemedium

A storage shelf holds $2$ -gallon paint cans and $5$ -gallon paint cans with a total of $41$ gallons. If there are $3$ of the $5$ -gallon cans on the shelf, how many $2$ -gallon cans are on the shelf?

The situation can be written as the system $\begin{cases} 2x + 5y = 41 \ y = 3 \end{cases}$ . Substitute $y = 3$ into the first equation: $2x + 5(3) = 41$ , so $2x + 15 = 41$ . Then $2x = 26$ and $x = 13$ .

Mid-gamemedium

A gardener purchased $\text{\char36}6$ flower pots and $\text{\char36}15$ trees for a total of $\text{\char36}138$ . If the gardener purchased $6$ trees, how many flower pots did the gardener buy?

The situation can be written as the system $\begin{cases} 6p + 15r = 138 \ r = 6 \end{cases}$ . Substitute $r = 6$ into the first equation: $6p + 15(6) = 138$ , so $6p + 90 = 138$ . Then $6p = 48$ and $p = 8$ .

Mid-gamemedium

A delivery includes $4$ -kilogram boxes and $7$ -kilogram boxes with a total mass of $67$ kilograms. If there are $5$ of the $7$ -kilogram boxes, how many $4$ -kilogram boxes are in the delivery?

The situation can be written as the system $\begin{cases} 4b + 7s = 67 \ s = 5 \end{cases}$ . Substitute $s = 5$ into the first equation: $4b + 7(5) = 67$ , so $4b + 35 = 67$ . Then $4b = 32$ and $b = 8$ .

Mid-gamemedium

A club sold $\text{\char36}3$ raffle tickets and $\text{\char36}10$ shirts for a total of $\text{\char36}149$ . If the club sold $8$ shirts, how many raffle tickets did the club sell?

The situation can be written as the system $\begin{cases} 3t + 10s = 149 \ s = 8 \end{cases}$ . Substitute $s = 8$ into the first equation: $3t + 10(8) = 149$ , so $3t + 80 = 149$ . Then $3t = 69$ and $t = 23$ .

Mid-gamemedium

A parking lot charges $\text{\char36}5$ per car and $\text{\char36}15$ per bus and collects a total of $\text{\char36}105$ . If the lot parks $4$ buses, how many cars does the lot park?

The situation can be written as the system $\begin{cases} 5c + 15b = 105 \ b = 4 \end{cases}$ . Substitute $b = 4$ into the first equation: $5c + 15(4) = 105$ , so $5c + 60 = 105$ . Then $5c = 45$ and $c = 9$ .

Mid-gamemedium

A media shelf holds DVDs that weigh $2$ pounds each and Blu-ray cases that weigh $5$ pounds each, with a total weight of $44$ pounds. If there are $6$ Blu-ray cases on the shelf, how many DVDs are on the shelf?

The situation can be written as the system $\begin{cases} 2d + 5r = 44 \ r = 6 \end{cases}$ . Substitute $r = 6$ into the first equation: $2d + 5(6) = 44$ , so $2d + 30 = 44$ . Then $2d = 14$ and $d = 7$ .

Buzzer beatermedium

A market order includes $\text{\char36}9$ chickens and $\text{\char36}20$ turkeys for a total of $\text{\char36}156$ . If the order includes $6$ turkeys, how many chickens are in the order?

The situation can be written as the system $\begin{cases} 9c + 20t = 156 \ t = 6 \end{cases}$ . Substitute $t = 6$ into the first equation: $9c + 20(6) = 156$ , so $9c + 120 = 156$ . Then $9c = 36$ and $c = 4$ .

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