QuestionA wireless store has 170 smartphone and 260 tablet preorders totaling \$1366. Find the cost of each device.

Studdy Solution

STEP 1

Assumptions1. The number of preorders for the smartphone is170. The number of preorders for the tablet is2603. The combined sale of the preorders for a smartphone and a tablet together is $13664. Each device (smartphone and tablet) has a fixed price

STEP 2

We can set up a system of linear equations to solve this problem. Let's denote the cost of one smartphone as $s$ and the cost of one tablet as $t$ . The total sales from the smartphones and tablets can be represented as $170s +260t =1366$

STEP 3

We only have one equation and two unknowns, so we can't solve this system directly. However, we can express one variable in terms of the other. Let's express $s$ in terms of $t$ $s = \frac{1366 -260t}{170}$

STEP 4

Now we have an equation for $s$ in terms of $t$ . However, we know that the cost of a smartphone or a tablet cannot be negative, so we can set up an inequality to find the possible values for $t$ $1366 -260t \geq0$

STEP 5

olving this inequality will give us the range of possible values for $t$ $t \leq \frac{136}{260}$

STEP 6

Calculate the maximum value for $t$ $t \leq \frac{1366}{260} \approx5.25$

STEP 7

Similarly, we can set up an inequality for $s$ $1366 -170s \geq0$

STEP 8

olving this inequality will give us the range of possible values for $s$ $s \leq \frac{1366}{170}$

STEP 9

Calculate the maximum value for $s$ $s \leq \frac{1366}{170} \approx8.04$

STEP 10

From the above calculations, we can see that the cost of one smartphone is less than or equal to approximately $8.04$ and the cost of one tablet is less than or equal to approximately $5.25$ . However, these are not integer values, and it is unlikely that the cost of a smartphone or a tablet would be a non-integer value. Therefore, we can conclude that there are no combinations of the number of products sold satisfying the given conditions.

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QuestionA wireless store has 170 smartphone and 260 tablet preorders totaling \$1366. Find the cost of each device.

Studdy Solution

STEP 1

Assumptions1. The number of preorders for the smartphone is170. The number of preorders for the tablet is2603. The combined sale of the preorders for a smartphone and a tablet together is $13664. Each device (smartphone and tablet) has a fixed price

STEP 2

We can set up a system of linear equations to solve this problem. Let's denote the cost of one smartphone as $s$ and the cost of one tablet as $t$ . The total sales from the smartphones and tablets can be represented as $170s +260t =1366$

STEP 3

We only have one equation and two unknowns, so we can't solve this system directly. However, we can express one variable in terms of the other. Let's express $s$ in terms of $t$ $s = \frac{1366 -260t}{170}$

STEP 4

Now we have an equation for $s$ in terms of $t$ . However, we know that the cost of a smartphone or a tablet cannot be negative, so we can set up an inequality to find the possible values for $t$ $1366 -260t \geq0$

STEP 5

olving this inequality will give us the range of possible values for $t$ $t \leq \frac{136}{260}$

STEP 6

Calculate the maximum value for $t$ $t \leq \frac{1366}{260} \approx5.25$

STEP 7

Similarly, we can set up an inequality for $s$ $1366 -170s \geq0$

STEP 8

olving this inequality will give us the range of possible values for $s$ $s \leq \frac{1366}{170}$

STEP 9

Calculate the maximum value for $s$ $s \leq \frac{1366}{170} \approx8.04$

STEP 10

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QuestionA wireless store has 170 smartphone and 260 tablet preorders totaling \$1366. Find the cost of each device.

Studdy Solution

STEP 1

Assumptions1. The number of preorders for the smartphone is170. The number of preorders for the tablet is2603. The combined sale of the preorders for a smartphone and a tablet together is $13664. Each device (smartphone and tablet) has a fixed price

STEP 2

We can set up a system of linear equations to solve this problem. Let's denote the cost of one smartphone as sss and the cost of one tablet as ttt. The total sales from the smartphones and tablets can be represented as170s+260t=1366170s +260t =1366170s+260t=1366

STEP 3

We only have one equation and two unknowns, so we can't solve this system directly. However, we can express one variable in terms of the other. Let's express sss in terms of ttts=1366−260t170s = \frac{1366 -260t}{170}s=1701366−260t​

STEP 4

Now we have an equation for sss in terms of ttt. However, we know that the cost of a smartphone or a tablet cannot be negative, so we can set up an inequality to find the possible values for ttt1366−260t≥01366 -260t \geq01366−260t≥0

STEP 5

olving this inequality will give us the range of possible values for tttt≤136260t \leq \frac{136}{260}t≤260136​

STEP 6

Calculate the maximum value for tttt≤1366260≈5.25t \leq \frac{1366}{260} \approx5.25t≤2601366​≈5.25

STEP 7

Similarly, we can set up an inequality for sss1366−170s≥01366 -170s \geq01366−170s≥0

STEP 8

olving this inequality will give us the range of possible values for ssss≤1366170s \leq \frac{1366}{170}s≤1701366​

STEP 9

Calculate the maximum value for ssss≤1366170≈8.04s \leq \frac{1366}{170} \approx8.04s≤1701366​≈8.04

STEP 10

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We can set up a system of linear equations to solve this problem. Let's denote the cost of one smartphone as $s$ and the cost of one tablet as $t$ . The total sales from the smartphones and tablets can be represented as $170s +260t =1366$

We only have one equation and two unknowns, so we can't solve this system directly. However, we can express one variable in terms of the other. Let's express $s$ in terms of $t$ $s = \frac{1366 -260t}{170}$

Now we have an equation for $s$ in terms of $t$ . However, we know that the cost of a smartphone or a tablet cannot be negative, so we can set up an inequality to find the possible values for $t$ $1366 -260t \geq0$

olving this inequality will give us the range of possible values for $t$ $t \leq \frac{136}{260}$

Calculate the maximum value for $t$ $t \leq \frac{1366}{260} \approx5.25$

Similarly, we can set up an inequality for $s$ $1366 -170s \geq0$

olving this inequality will give us the range of possible values for $s$ $s \leq \frac{1366}{170}$

Calculate the maximum value for $s$ $s \leq \frac{1366}{170} \approx8.04$